Step |
Hyp |
Ref |
Expression |
1 |
|
eldiophb |
|
2 |
|
simp-5r |
|
3 |
|
simprr |
|
4 |
3
|
ad2antrr |
|
5 |
|
simprl |
|
6 |
|
f1f |
|
7 |
5 6
|
syl |
|
8 |
|
mzprename |
|
9 |
2 4 7 8
|
syl3anc |
|
10 |
|
simprr |
|
11 |
|
diophrw |
|
12 |
11
|
eqcomd |
|
13 |
2 5 10 12
|
syl3anc |
|
14 |
|
fveq1 |
|
15 |
14
|
eqeq1d |
|
16 |
15
|
anbi2d |
|
17 |
16
|
rexbidv |
|
18 |
17
|
abbidv |
|
19 |
18
|
rspceeqv |
|
20 |
9 13 19
|
syl2anc |
|
21 |
|
simplll |
|
22 |
|
simplrl |
|
23 |
|
simplrr |
|
24 |
|
simprl |
|
25 |
|
eldioph2lem2 |
|
26 |
21 22 23 24 25
|
syl22anc |
|
27 |
|
rexv |
|
28 |
26 27
|
sylibr |
|
29 |
20 28
|
r19.29a |
|
30 |
|
eqeq1 |
|
31 |
30
|
rexbidv |
|
32 |
29 31
|
syl5ibrcom |
|
33 |
32
|
rexlimdvva |
|
34 |
33
|
adantld |
|
35 |
1 34
|
syl5bi |
|
36 |
|
simpr |
|
37 |
|
simplll |
|
38 |
|
simpllr |
|
39 |
|
simplrr |
|
40 |
|
simpr |
|
41 |
|
eldioph2 |
|
42 |
37 38 39 40 41
|
syl121anc |
|
43 |
42
|
adantr |
|
44 |
36 43
|
eqeltrd |
|
45 |
44
|
rexlimdva2 |
|
46 |
35 45
|
impbid |
|