Step |
Hyp |
Ref |
Expression |
1 |
|
ensym |
|
2 |
|
bren |
|
3 |
1 2
|
sylib |
|
4 |
|
ssid |
|
5 |
|
sseq1 |
|
6 |
5
|
anbi1d |
|
7 |
6
|
anbi1d |
|
8 |
|
uneq1 |
|
9 |
|
imaeq2 |
|
10 |
9
|
uneq1d |
|
11 |
8 10
|
breq12d |
|
12 |
11
|
bibi1d |
|
13 |
7 12
|
imbi12d |
|
14 |
|
sseq1 |
|
15 |
14
|
anbi1d |
|
16 |
15
|
anbi1d |
|
17 |
|
uneq1 |
|
18 |
|
imaeq2 |
|
19 |
18
|
uneq1d |
|
20 |
17 19
|
breq12d |
|
21 |
20
|
bibi1d |
|
22 |
16 21
|
imbi12d |
|
23 |
|
sseq1 |
|
24 |
23
|
anbi1d |
|
25 |
24
|
anbi1d |
|
26 |
|
uneq1 |
|
27 |
|
imaeq2 |
|
28 |
27
|
uneq1d |
|
29 |
26 28
|
breq12d |
|
30 |
29
|
bibi1d |
|
31 |
25 30
|
imbi12d |
|
32 |
|
sseq1 |
|
33 |
32
|
anbi1d |
|
34 |
33
|
anbi1d |
|
35 |
|
uneq1 |
|
36 |
|
imaeq2 |
|
37 |
36
|
uneq1d |
|
38 |
35 37
|
breq12d |
|
39 |
38
|
bibi1d |
|
40 |
34 39
|
imbi12d |
|
41 |
|
uncom |
|
42 |
|
un0 |
|
43 |
41 42
|
eqtri |
|
44 |
|
ima0 |
|
45 |
44
|
uneq1i |
|
46 |
|
uncom |
|
47 |
|
un0 |
|
48 |
46 47
|
eqtri |
|
49 |
45 48
|
eqtri |
|
50 |
43 49
|
breq12i |
|
51 |
50
|
a1i |
|
52 |
|
ssun1 |
|
53 |
|
sstr2 |
|
54 |
52 53
|
ax-mp |
|
55 |
54
|
anim1i |
|
56 |
55
|
anim1i |
|
57 |
56
|
imim1i |
|
58 |
|
uncom |
|
59 |
58
|
uneq1i |
|
60 |
|
unass |
|
61 |
59 60
|
eqtri |
|
62 |
61
|
a1i |
|
63 |
|
imaundi |
|
64 |
|
simprlr |
|
65 |
|
f1ofn |
|
66 |
64 65
|
syl |
|
67 |
|
ssun2 |
|
68 |
|
sstr2 |
|
69 |
67 68
|
ax-mp |
|
70 |
|
vex |
|
71 |
70
|
snss |
|
72 |
69 71
|
sylibr |
|
73 |
72
|
adantr |
|
74 |
73
|
ad2antrl |
|
75 |
|
fnsnfv |
|
76 |
66 74 75
|
syl2anc |
|
77 |
76
|
eqcomd |
|
78 |
77
|
uneq2d |
|
79 |
63 78
|
eqtrid |
|
80 |
79
|
uneq1d |
|
81 |
|
uncom |
|
82 |
81
|
uneq1i |
|
83 |
|
unass |
|
84 |
82 83
|
eqtri |
|
85 |
80 84
|
eqtrdi |
|
86 |
62 85
|
breq12d |
|
87 |
|
simplr |
|
88 |
|
incom |
|
89 |
|
simprrl |
|
90 |
88 89
|
eqtrid |
|
91 |
|
minel |
|
92 |
74 90 91
|
syl2anc |
|
93 |
|
ioran |
|
94 |
|
elun |
|
95 |
93 94
|
xchnxbir |
|
96 |
87 92 95
|
sylanbrc |
|
97 |
|
simplr |
|
98 |
|
f1of1 |
|
99 |
98
|
adantl |
|
100 |
54
|
adantr |
|
101 |
|
f1elima |
|
102 |
99 73 100 101
|
syl3anc |
|
103 |
102
|
biimpd |
|
104 |
103
|
adantl |
|
105 |
97 104
|
mtod |
|
106 |
105
|
adantrr |
|
107 |
|
f1of |
|
108 |
64 107
|
syl |
|
109 |
108 74
|
ffvelrnd |
|
110 |
|
incom |
|
111 |
|
simprrr |
|
112 |
110 111
|
eqtrid |
|
113 |
|
minel |
|
114 |
109 112 113
|
syl2anc |
|
115 |
|
ioran |
|
116 |
|
elun |
|
117 |
115 116
|
xchnxbir |
|
118 |
106 114 117
|
sylanbrc |
|
119 |
|
fvex |
|
120 |
70 119
|
domunsncan |
|
121 |
96 118 120
|
syl2anc |
|
122 |
86 121
|
bitrd |
|
123 |
|
bitr |
|
124 |
123
|
ex |
|
125 |
122 124
|
syl |
|
126 |
125
|
ex |
|
127 |
126
|
a2d |
|
128 |
57 127
|
syl5 |
|
129 |
13 22 31 40 51 128
|
findcard2s |
|
130 |
129
|
expd |
|
131 |
4 130
|
mpani |
|
132 |
131
|
3imp |
|
133 |
|
f1ofo |
|
134 |
|
foima |
|
135 |
133 134
|
syl |
|
136 |
135
|
uneq1d |
|
137 |
136
|
breq2d |
|
138 |
137
|
bibi1d |
|
139 |
138
|
3ad2ant2 |
|
140 |
132 139
|
mpbid |
|
141 |
140
|
3exp |
|
142 |
141
|
exlimdv |
|
143 |
3 142
|
syl5 |
|
144 |
143
|
imp31 |
|