Step |
Hyp |
Ref |
Expression |
1 |
|
ptcmp.1 |
|
2 |
|
ptcmp.2 |
|
3 |
|
ptcmp.3 |
|
4 |
|
ptcmp.4 |
|
5 |
|
ptcmp.5 |
|
6 |
|
ptcmplem2.5 |
|
7 |
|
ptcmplem2.6 |
|
8 |
|
ptcmplem2.7 |
|
9 |
|
0ss |
|
10 |
|
0fin |
|
11 |
|
elfpw |
|
12 |
9 10 11
|
mpbir2an |
|
13 |
|
unieq |
|
14 |
|
uni0 |
|
15 |
13 14
|
eqtrdi |
|
16 |
15
|
rspceeqv |
|
17 |
12 16
|
mpan |
|
18 |
17
|
necon3bi |
|
19 |
8 18
|
syl |
|
20 |
|
n0 |
|
21 |
19 20
|
sylib |
|
22 |
|
fveq2 |
|
23 |
22
|
unieqd |
|
24 |
23
|
cbvixpv |
|
25 |
2 24
|
eqtri |
|
26 |
5
|
elin2d |
|
27 |
26
|
adantr |
|
28 |
25 27
|
eqeltrrid |
|
29 |
|
ssrab2 |
|
30 |
19
|
adantr |
|
31 |
25 30
|
eqnetrrid |
|
32 |
|
eqid |
|
33 |
32
|
resixpfo |
|
34 |
29 31 33
|
sylancr |
|
35 |
|
fonum |
|
36 |
28 34 35
|
syl2anc |
|
37 |
|
vex |
|
38 |
|
difexg |
|
39 |
37 38
|
mp1i |
|
40 |
|
dmexg |
|
41 |
|
uniexg |
|
42 |
39 40 41
|
3syl |
|
43 |
42
|
ralrimivw |
|
44 |
|
eqid |
|
45 |
44
|
fnmpt |
|
46 |
43 45
|
syl |
|
47 |
|
dffn4 |
|
48 |
46 47
|
sylib |
|
49 |
|
fonum |
|
50 |
27 48 49
|
syl2anc |
|
51 |
|
ssdif0 |
|
52 |
|
simpr |
|
53 |
|
simpr |
|
54 |
53 25
|
eleqtrdi |
|
55 |
|
vex |
|
56 |
55
|
elixp |
|
57 |
56
|
simprbi |
|
58 |
54 57
|
syl |
|
59 |
58
|
r19.21bi |
|
60 |
59
|
snssd |
|
61 |
60
|
adantr |
|
62 |
52 61
|
eqssd |
|
63 |
|
fvex |
|
64 |
63
|
ensn1 |
|
65 |
62 64
|
eqbrtrdi |
|
66 |
65
|
ex |
|
67 |
51 66
|
syl5bir |
|
68 |
67
|
con3d |
|
69 |
|
neq0 |
|
70 |
68 69
|
syl6ib |
|
71 |
|
eldifi |
|
72 |
|
simplr |
|
73 |
|
iftrue |
|
74 |
73 23
|
eleq12d |
|
75 |
72 74
|
syl5ibrcom |
|
76 |
53 2
|
eleqtrdi |
|
77 |
55
|
elixp |
|
78 |
77
|
simprbi |
|
79 |
76 78
|
syl |
|
80 |
79
|
ad2antrr |
|
81 |
80
|
r19.21bi |
|
82 |
|
iffalse |
|
83 |
82
|
eleq1d |
|
84 |
81 83
|
syl5ibrcom |
|
85 |
75 84
|
pm2.61d |
|
86 |
85
|
ralrimiva |
|
87 |
3
|
ad3antrrr |
|
88 |
|
mptelixpg |
|
89 |
87 88
|
syl |
|
90 |
86 89
|
mpbird |
|
91 |
90 2
|
eleqtrrdi |
|
92 |
71 91
|
sylan2 |
|
93 |
|
vex |
|
94 |
93
|
unisn |
|
95 |
|
simplr |
|
96 |
|
eleq1w |
|
97 |
95 96
|
syl5ibrcom |
|
98 |
97
|
pm4.71rd |
|
99 |
|
equequ1 |
|
100 |
|
fveq2 |
|
101 |
99 100
|
ifbieq2d |
|
102 |
|
eqid |
|
103 |
|
vex |
|
104 |
|
fvex |
|
105 |
103 104
|
ifex |
|
106 |
101 102 105
|
fvmpt |
|
107 |
106
|
neeq1d |
|
108 |
107
|
adantl |
|
109 |
|
iffalse |
|
110 |
109
|
necon1ai |
|
111 |
|
eldifsni |
|
112 |
111
|
ad2antlr |
|
113 |
|
iftrue |
|
114 |
|
fveq2 |
|
115 |
113 114
|
neeq12d |
|
116 |
112 115
|
syl5ibrcom |
|
117 |
110 116
|
impbid2 |
|
118 |
108 117
|
bitrd |
|
119 |
118
|
pm5.32da |
|
120 |
98 119
|
bitr4d |
|
121 |
120
|
abbidv |
|
122 |
|
df-sn |
|
123 |
|
df-rab |
|
124 |
121 122 123
|
3eqtr4g |
|
125 |
|
fvex |
|
126 |
103 125
|
ifex |
|
127 |
126
|
rgenw |
|
128 |
102
|
fnmpt |
|
129 |
127 128
|
mp1i |
|
130 |
|
ixpfn |
|
131 |
76 130
|
syl |
|
132 |
131
|
ad2antrr |
|
133 |
|
fndmdif |
|
134 |
129 132 133
|
syl2anc |
|
135 |
124 134
|
eqtr4d |
|
136 |
135
|
unieqd |
|
137 |
94 136
|
syl5eqr |
|
138 |
|
difeq1 |
|
139 |
138
|
dmeqd |
|
140 |
139
|
unieqd |
|
141 |
140
|
rspceeqv |
|
142 |
92 137 141
|
syl2anc |
|
143 |
142
|
ex |
|
144 |
143
|
exlimdv |
|
145 |
70 144
|
syld |
|
146 |
145
|
expimpd |
|
147 |
23
|
breq1d |
|
148 |
147
|
notbid |
|
149 |
148
|
elrab |
|
150 |
44
|
elrnmpt |
|
151 |
150
|
elv |
|
152 |
146 149 151
|
3imtr4g |
|
153 |
152
|
ssrdv |
|
154 |
|
ssnum |
|
155 |
50 153 154
|
syl2anc |
|
156 |
|
xpnum |
|
157 |
36 155 156
|
syl2anc |
|
158 |
3
|
adantr |
|
159 |
|
rabexg |
|
160 |
158 159
|
syl |
|
161 |
|
fvex |
|
162 |
161
|
uniex |
|
163 |
162
|
rgenw |
|
164 |
|
iunexg |
|
165 |
160 163 164
|
sylancl |
|
166 |
|
resixp |
|
167 |
29 54 166
|
sylancr |
|
168 |
167
|
ne0d |
|
169 |
|
ixpiunwdom |
|
170 |
160 165 168 169
|
syl3anc |
|
171 |
|
numwdom |
|
172 |
157 170 171
|
syl2anc |
|
173 |
21 172
|
exlimddv |
|