Step |
Hyp |
Ref |
Expression |
1 |
|
symgext.s |
|
2 |
|
symgext.e |
|
3 |
1 2
|
symgextf |
|
4 |
|
difsnid |
|
5 |
4
|
eqcomd |
|
6 |
5
|
eleq2d |
|
7 |
5
|
eleq2d |
|
8 |
6 7
|
anbi12d |
|
9 |
8
|
adantr |
|
10 |
|
elun |
|
11 |
|
elun |
|
12 |
1 2
|
symgextfv |
|
13 |
12
|
com12 |
|
14 |
13
|
adantr |
|
15 |
14
|
imp |
|
16 |
1 2
|
symgextfv |
|
17 |
16
|
com12 |
|
18 |
17
|
adantl |
|
19 |
18
|
imp |
|
20 |
15 19
|
eqeq12d |
|
21 |
|
eqid |
|
22 |
21 1
|
symgbasf1o |
|
23 |
|
f1of1 |
|
24 |
|
dff13 |
|
25 |
|
fveqeq2 |
|
26 |
|
equequ1 |
|
27 |
25 26
|
imbi12d |
|
28 |
|
fveq2 |
|
29 |
28
|
eqeq2d |
|
30 |
|
equequ2 |
|
31 |
29 30
|
imbi12d |
|
32 |
27 31
|
rspc2va |
|
33 |
32
|
expcom |
|
34 |
33
|
a1d |
|
35 |
24 34
|
simplbiim |
|
36 |
22 23 35
|
3syl |
|
37 |
36
|
impcom |
|
38 |
37
|
impcom |
|
39 |
20 38
|
sylbid |
|
40 |
39
|
ex |
|
41 |
1 2
|
symgextf1lem |
|
42 |
|
eqneqall |
|
43 |
42
|
eqcoms |
|
44 |
43
|
com12 |
|
45 |
41 44
|
syl6com |
|
46 |
45
|
ancoms |
|
47 |
1 2
|
symgextf1lem |
|
48 |
|
eqneqall |
|
49 |
48
|
com12 |
|
50 |
47 49
|
syl6com |
|
51 |
|
elsni |
|
52 |
|
elsni |
|
53 |
|
eqtr3 |
|
54 |
53
|
2a1d |
|
55 |
51 52 54
|
syl2an |
|
56 |
40 46 50 55
|
ccase |
|
57 |
10 11 56
|
syl2anb |
|
58 |
57
|
com12 |
|
59 |
9 58
|
sylbid |
|
60 |
59
|
ralrimivv |
|
61 |
|
dff13 |
|
62 |
3 60 61
|
sylanbrc |
|