Step |
Hyp |
Ref |
Expression |
1 |
|
unss |
|
2 |
|
simpl |
|
3 |
1 2
|
sylbir |
|
4 |
|
vex |
|
5 |
|
trcleq2lem |
|
6 |
4 5
|
elab |
|
7 |
6
|
biimpri |
|
8 |
3 7
|
sylan |
|
9 |
|
intss1 |
|
10 |
8 9
|
syl |
|
11 |
|
simpr |
|
12 |
1 11
|
sylbir |
|
13 |
|
trcleq2lem |
|
14 |
4 13
|
elab |
|
15 |
14
|
biimpri |
|
16 |
12 15
|
sylan |
|
17 |
|
intss1 |
|
18 |
16 17
|
syl |
|
19 |
10 18
|
unssd |
|
20 |
|
simpr |
|
21 |
19 20
|
jca |
|
22 |
|
ssmin |
|
23 |
|
ssmin |
|
24 |
|
unss12 |
|
25 |
22 23 24
|
mp2an |
|
26 |
|
sstr |
|
27 |
25 26
|
mpan |
|
28 |
27
|
anim1i |
|
29 |
21 28
|
impbii |
|
30 |
29
|
abbii |
|
31 |
30
|
inteqi |
|
32 |
|
unexg |
|
33 |
|
trclfv |
|
34 |
32 33
|
syl |
|
35 |
|
simpl |
|
36 |
|
trclfv |
|
37 |
35 36
|
syl |
|
38 |
|
simpr |
|
39 |
|
trclfv |
|
40 |
38 39
|
syl |
|
41 |
37 40
|
uneq12d |
|
42 |
41
|
fveq2d |
|
43 |
|
fvex |
|
44 |
36 43
|
eqeltrrdi |
|
45 |
|
fvex |
|
46 |
39 45
|
eqeltrrdi |
|
47 |
|
unexg |
|
48 |
44 46 47
|
syl2an |
|
49 |
|
trclfv |
|
50 |
48 49
|
syl |
|
51 |
42 50
|
eqtrd |
|
52 |
31 34 51
|
3eqtr4a |
|