Step |
Hyp |
Ref |
Expression |
1 |
|
dfsalgen2.1 |
|
2 |
|
id |
|
3 |
2
|
eqcomd |
|
4 |
3
|
adantl |
|
5 |
|
salgencl |
|
6 |
1 5
|
syl |
|
7 |
6
|
adantr |
|
8 |
4 7
|
eqeltrd |
|
9 |
|
unieq |
|
10 |
9
|
adantl |
|
11 |
1
|
adantr |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
11 12 13
|
salgenuni |
|
15 |
10 14
|
eqtr3d |
|
16 |
12
|
sssalgen |
|
17 |
11 16
|
syl |
|
18 |
|
simpr |
|
19 |
17 18
|
sseqtrd |
|
20 |
8 15 19
|
3jca |
|
21 |
4
|
ad2antrr |
|
22 |
21
|
adantrl |
|
23 |
11
|
ad2antrr |
|
24 |
23
|
adantrl |
|
25 |
|
simplr |
|
26 |
25
|
adantrl |
|
27 |
|
simpr |
|
28 |
27
|
adantrl |
|
29 |
|
simprl |
|
30 |
24 12 26 28 29
|
salgenss |
|
31 |
22 30
|
eqsstrd |
|
32 |
31
|
ex |
|
33 |
32
|
ralrimiva |
|
34 |
20 33
|
jca |
|
35 |
34
|
ex |
|
36 |
1
|
adantr |
|
37 |
|
simprl1 |
|
38 |
|
simprl2 |
|
39 |
|
simprl3 |
|
40 |
|
unieq |
|
41 |
40
|
eqeq1d |
|
42 |
|
sseq2 |
|
43 |
41 42
|
anbi12d |
|
44 |
|
sseq2 |
|
45 |
43 44
|
imbi12d |
|
46 |
45
|
cbvralvw |
|
47 |
46
|
biimpi |
|
48 |
47
|
adantr |
|
49 |
|
simpr |
|
50 |
48 49
|
jca |
|
51 |
50
|
3ad2antr1 |
|
52 |
|
3simpc |
|
53 |
52
|
adantl |
|
54 |
|
rspa |
|
55 |
51 53 54
|
sylc |
|
56 |
55
|
adantll |
|
57 |
56
|
adantll |
|
58 |
36 37 38 39 57
|
issalgend |
|
59 |
58
|
ex |
|
60 |
35 59
|
impbid |
|