Step |
Hyp |
Ref |
Expression |
1 |
|
psgnunilem1.t |
|
2 |
|
psgnunilem1.d |
|
3 |
|
psgnunilem1.p |
|
4 |
|
psgnunilem1.q |
|
5 |
|
psgnunilem1.a |
|
6 |
|
eqid |
|
7 |
6 1
|
pmtrfinv |
|
8 |
4 7
|
syl |
|
9 |
|
coeq1 |
|
10 |
9
|
eqeq1d |
|
11 |
8 10
|
syl5ibrcom |
|
12 |
11
|
adantr |
|
13 |
12
|
imp |
|
14 |
13
|
orcd |
|
15 |
6 1
|
pmtrfcnv |
|
16 |
3 15
|
syl |
|
17 |
16
|
eqcomd |
|
18 |
17
|
coeq2d |
|
19 |
6 1
|
pmtrff1o |
|
20 |
3 19
|
syl |
|
21 |
6 1
|
pmtrfconj |
|
22 |
4 20 21
|
syl2anc |
|
23 |
18 22
|
eqeltrd |
|
24 |
23
|
ad2antrr |
|
25 |
3
|
ad2antrr |
|
26 |
|
coass |
|
27 |
6 1
|
pmtrfinv |
|
28 |
3 27
|
syl |
|
29 |
28
|
coeq2d |
|
30 |
|
f1of |
|
31 |
20 30
|
syl |
|
32 |
6 1
|
pmtrff1o |
|
33 |
4 32
|
syl |
|
34 |
|
f1of |
|
35 |
33 34
|
syl |
|
36 |
|
fco |
|
37 |
31 35 36
|
syl2anc |
|
38 |
|
fcoi1 |
|
39 |
37 38
|
syl |
|
40 |
29 39
|
eqtrd |
|
41 |
26 40
|
eqtr2id |
|
42 |
41
|
ad2antrr |
|
43 |
5
|
ad2antrr |
|
44 |
20
|
adantr |
|
45 |
33
|
adantr |
|
46 |
6 1
|
pmtrfb |
|
47 |
46
|
simp3bi |
|
48 |
3 47
|
syl |
|
49 |
48
|
adantr |
|
50 |
|
2onn |
|
51 |
|
nnfi |
|
52 |
50 51
|
ax-mp |
|
53 |
6 1
|
pmtrfb |
|
54 |
53
|
simp3bi |
|
55 |
4 54
|
syl |
|
56 |
|
enfi |
|
57 |
55 56
|
syl |
|
58 |
52 57
|
mpbiri |
|
59 |
58
|
adantr |
|
60 |
5
|
adantr |
|
61 |
|
en2eleq |
|
62 |
60 49 61
|
syl2anc |
|
63 |
|
simprl |
|
64 |
|
f1ofn |
|
65 |
20 64
|
syl |
|
66 |
65
|
adantr |
|
67 |
|
fimass |
|
68 |
31 67
|
syl |
|
69 |
68
|
adantr |
|
70 |
|
simprr |
|
71 |
|
fnfvima |
|
72 |
66 69 70 71
|
syl3anc |
|
73 |
|
difss |
|
74 |
|
dmss |
|
75 |
73 74
|
ax-mp |
|
76 |
|
f1odm |
|
77 |
20 76
|
syl |
|
78 |
75 77
|
sseqtrid |
|
79 |
78 5
|
sseldd |
|
80 |
|
eqid |
|
81 |
6 1 80
|
pmtrffv |
|
82 |
3 79 81
|
syl2anc |
|
83 |
5
|
iftrued |
|
84 |
82 83
|
eqtrd |
|
85 |
84
|
adantr |
|
86 |
|
imaco |
|
87 |
28
|
imaeq1d |
|
88 |
|
difss |
|
89 |
|
dmss |
|
90 |
88 89
|
ax-mp |
|
91 |
|
f1odm |
|
92 |
90 91
|
sseqtrid |
|
93 |
33 92
|
syl |
|
94 |
|
resiima |
|
95 |
93 94
|
syl |
|
96 |
87 95
|
eqtrd |
|
97 |
86 96
|
eqtr3id |
|
98 |
97
|
adantr |
|
99 |
72 85 98
|
3eltr3d |
|
100 |
63 99
|
prssd |
|
101 |
62 100
|
eqsstrd |
|
102 |
55
|
ensymd |
|
103 |
|
entr |
|
104 |
48 102 103
|
syl2anc |
|
105 |
104
|
adantr |
|
106 |
|
fisseneq |
|
107 |
59 101 105 106
|
syl3anc |
|
108 |
107
|
eqcomd |
|
109 |
|
f1otrspeq |
|
110 |
44 45 49 108 109
|
syl22anc |
|
111 |
110
|
expr |
|
112 |
111
|
necon3ad |
|
113 |
112
|
imp |
|
114 |
18
|
difeq1d |
|
115 |
114
|
dmeqd |
|
116 |
|
f1omvdconj |
|
117 |
35 20 116
|
syl2anc |
|
118 |
115 117
|
eqtrd |
|
119 |
118
|
eleq2d |
|
120 |
119
|
ad2antrr |
|
121 |
113 120
|
mtbird |
|
122 |
|
coeq1 |
|
123 |
122
|
eqeq2d |
|
124 |
|
difeq1 |
|
125 |
124
|
dmeqd |
|
126 |
125
|
eleq2d |
|
127 |
126
|
notbid |
|
128 |
123 127
|
3anbi13d |
|
129 |
|
coeq2 |
|
130 |
129
|
eqeq2d |
|
131 |
|
difeq1 |
|
132 |
131
|
dmeqd |
|
133 |
132
|
eleq2d |
|
134 |
130 133
|
3anbi12d |
|
135 |
128 134
|
rspc2ev |
|
136 |
24 25 42 43 121 135
|
syl113anc |
|
137 |
136
|
olcd |
|
138 |
14 137
|
pm2.61dane |
|
139 |
4
|
adantr |
|
140 |
|
coass |
|
141 |
6 1
|
pmtrfcnv |
|
142 |
4 141
|
syl |
|
143 |
142
|
eqcomd |
|
144 |
143
|
coeq2d |
|
145 |
140 144
|
eqtr3id |
|
146 |
6 1
|
pmtrfconj |
|
147 |
3 33 146
|
syl2anc |
|
148 |
145 147
|
eqeltrd |
|
149 |
148
|
adantr |
|
150 |
8
|
coeq1d |
|
151 |
|
fcoi2 |
|
152 |
37 151
|
syl |
|
153 |
150 152
|
eqtr2d |
|
154 |
|
coass |
|
155 |
153 154
|
eqtrdi |
|
156 |
155
|
adantr |
|
157 |
|
f1ofn |
|
158 |
33 157
|
syl |
|
159 |
|
fnelnfp |
|
160 |
158 79 159
|
syl2anc |
|
161 |
160
|
necon2bbid |
|
162 |
161
|
biimpar |
|
163 |
|
fnfvima |
|
164 |
158 78 5 163
|
syl3anc |
|
165 |
164
|
adantr |
|
166 |
162 165
|
eqeltrrd |
|
167 |
145
|
difeq1d |
|
168 |
167
|
dmeqd |
|
169 |
|
f1omvdconj |
|
170 |
31 33 169
|
syl2anc |
|
171 |
168 170
|
eqtrd |
|
172 |
171
|
adantr |
|
173 |
166 172
|
eleqtrrd |
|
174 |
|
simpr |
|
175 |
|
coeq1 |
|
176 |
175
|
eqeq2d |
|
177 |
|
difeq1 |
|
178 |
177
|
dmeqd |
|
179 |
178
|
eleq2d |
|
180 |
179
|
notbid |
|
181 |
176 180
|
3anbi13d |
|
182 |
|
coeq2 |
|
183 |
182
|
eqeq2d |
|
184 |
|
difeq1 |
|
185 |
184
|
dmeqd |
|
186 |
185
|
eleq2d |
|
187 |
183 186
|
3anbi12d |
|
188 |
181 187
|
rspc2ev |
|
189 |
139 149 156 173 174 188
|
syl113anc |
|
190 |
189
|
olcd |
|
191 |
138 190
|
pm2.61dan |
|