Step |
Hyp |
Ref |
Expression |
1 |
|
xpord2.1 |
|
2 |
|
poxp2.1 |
|
3 |
|
poxp2.2 |
|
4 |
|
elxp2 |
|
5 |
|
equid |
|
6 |
|
equid |
|
7 |
5 6
|
pm3.2i |
|
8 |
|
neorian |
|
9 |
8
|
con2bii |
|
10 |
7 9
|
mpbi |
|
11 |
|
simp3 |
|
12 |
10 11
|
mto |
|
13 |
|
simp3 |
|
14 |
12 13
|
mto |
|
15 |
1
|
xpord2lem |
|
16 |
14 15
|
mtbir |
|
17 |
|
breq12 |
|
18 |
17
|
anidms |
|
19 |
16 18
|
mtbiri |
|
20 |
19
|
rexlimivw |
|
21 |
20
|
rexlimivw |
|
22 |
4 21
|
sylbi |
|
23 |
22
|
adantl |
|
24 |
|
3reeanv |
|
25 |
|
3reeanv |
|
26 |
25
|
rexbii |
|
27 |
26
|
2rexbii |
|
28 |
|
elxp2 |
|
29 |
|
elxp2 |
|
30 |
4 28 29
|
3anbi123i |
|
31 |
24 27 30
|
3bitr4ri |
|
32 |
|
df-3an |
|
33 |
|
simp3 |
|
34 |
|
simp3 |
|
35 |
|
simpr1l |
|
36 |
35
|
adantr |
|
37 |
|
simpr2r |
|
38 |
37
|
adantr |
|
39 |
36 38
|
jca |
|
40 |
|
simpr2l |
|
41 |
40
|
adantr |
|
42 |
|
simpr3r |
|
43 |
42
|
adantr |
|
44 |
41 43
|
jca |
|
45 |
2
|
ad2antrr |
|
46 |
|
simpr1r |
|
47 |
46
|
adantr |
|
48 |
|
potr |
|
49 |
45 36 47 41 48
|
syl13anc |
|
50 |
|
orc |
|
51 |
49 50
|
syl6 |
|
52 |
51
|
expd |
|
53 |
|
breq1 |
|
54 |
53 50
|
syl6bir |
|
55 |
54
|
a1i |
|
56 |
|
simprl1 |
|
57 |
52 55 56
|
mpjaod |
|
58 |
|
breq2 |
|
59 |
|
equequ2 |
|
60 |
58 59
|
orbi12d |
|
61 |
56 60
|
syl5ibcom |
|
62 |
|
simprr1 |
|
63 |
57 61 62
|
mpjaod |
|
64 |
3
|
ad2antrr |
|
65 |
|
simpr3l |
|
66 |
65
|
adantr |
|
67 |
|
potr |
|
68 |
64 38 66 43 67
|
syl13anc |
|
69 |
|
orc |
|
70 |
68 69
|
syl6 |
|
71 |
70
|
expd |
|
72 |
|
breq1 |
|
73 |
72 69
|
syl6bir |
|
74 |
73
|
a1i |
|
75 |
|
simprl2 |
|
76 |
71 74 75
|
mpjaod |
|
77 |
|
breq2 |
|
78 |
|
equequ2 |
|
79 |
77 78
|
orbi12d |
|
80 |
75 79
|
syl5ibcom |
|
81 |
|
simprr2 |
|
82 |
76 80 81
|
mpjaod |
|
83 |
|
simprr3 |
|
84 |
|
neorian |
|
85 |
83 84
|
sylib |
|
86 |
|
neorian |
|
87 |
86
|
con2bii |
|
88 |
|
breq1 |
|
89 |
|
equequ1 |
|
90 |
88 89
|
orbi12d |
|
91 |
90
|
adantr |
|
92 |
|
breq1 |
|
93 |
|
equequ1 |
|
94 |
92 93
|
orbi12d |
|
95 |
94
|
adantl |
|
96 |
|
neeq1 |
|
97 |
96
|
adantr |
|
98 |
|
neeq1 |
|
99 |
98
|
adantl |
|
100 |
97 99
|
orbi12d |
|
101 |
91 95 100
|
3anbi123d |
|
102 |
101
|
anbi1d |
|
103 |
102
|
anbi2d |
|
104 |
|
simprl1 |
|
105 |
|
simprr1 |
|
106 |
|
orcom |
|
107 |
|
ordi |
|
108 |
|
orcom |
|
109 |
|
equcom |
|
110 |
109
|
orbi2i |
|
111 |
108 110
|
bitri |
|
112 |
|
orcom |
|
113 |
111 112
|
anbi12i |
|
114 |
106 107 113
|
3bitri |
|
115 |
104 105 114
|
sylanbrc |
|
116 |
2
|
ad2antrr |
|
117 |
40
|
adantr |
|
118 |
46
|
adantr |
|
119 |
|
po2nr |
|
120 |
116 117 118 119
|
syl12anc |
|
121 |
115 120
|
orcnd |
|
122 |
|
simprl2 |
|
123 |
|
simprr2 |
|
124 |
|
orcom |
|
125 |
|
ordi |
|
126 |
|
orcom |
|
127 |
|
equcom |
|
128 |
127
|
orbi2i |
|
129 |
126 128
|
bitri |
|
130 |
|
orcom |
|
131 |
129 130
|
anbi12i |
|
132 |
124 125 131
|
3bitri |
|
133 |
122 123 132
|
sylanbrc |
|
134 |
3
|
ad2antrr |
|
135 |
42
|
adantr |
|
136 |
65
|
adantr |
|
137 |
|
po2nr |
|
138 |
134 135 136 137
|
syl12anc |
|
139 |
133 138
|
orcnd |
|
140 |
121 139
|
jca |
|
141 |
103 140
|
syl6bi |
|
142 |
141
|
com12 |
|
143 |
87 142
|
syl5bir |
|
144 |
85 143
|
mt3d |
|
145 |
63 82 144
|
3jca |
|
146 |
39 44 145
|
3jca |
|
147 |
146
|
ex |
|
148 |
33 34 147
|
syl2ani |
|
149 |
|
breq12 |
|
150 |
149
|
3adant3 |
|
151 |
1
|
xpord2lem |
|
152 |
150 151
|
bitrdi |
|
153 |
|
breq12 |
|
154 |
153
|
3adant1 |
|
155 |
1
|
xpord2lem |
|
156 |
154 155
|
bitrdi |
|
157 |
152 156
|
anbi12d |
|
158 |
|
breq12 |
|
159 |
158
|
3adant2 |
|
160 |
1
|
xpord2lem |
|
161 |
159 160
|
bitrdi |
|
162 |
157 161
|
imbi12d |
|
163 |
148 162
|
syl5ibrcom |
|
164 |
32 163
|
sylan2br |
|
165 |
164
|
anassrs |
|
166 |
165
|
rexlimdvva |
|
167 |
166
|
anassrs |
|
168 |
167
|
rexlimdvva |
|
169 |
168
|
rexlimdvva |
|
170 |
169
|
imp |
|
171 |
31 170
|
sylan2b |
|
172 |
23 171
|
ispod |
|