Step |
Hyp |
Ref |
Expression |
1 |
|
projf1o.1 |
|
2 |
|
projf1o.2 |
|
3 |
|
snidg |
|
4 |
1 3
|
syl |
|
5 |
4
|
adantr |
|
6 |
|
simpr |
|
7 |
5 6
|
opelxpd |
|
8 |
|
opeq2 |
|
9 |
8
|
cbvmptv |
|
10 |
2 9
|
eqtri |
|
11 |
7 10
|
fmptd |
|
12 |
|
simpl1 |
|
13 |
2 8 6 7
|
fvmptd3 |
|
14 |
13
|
eqcomd |
|
15 |
14
|
3adant3 |
|
16 |
15
|
adantr |
|
17 |
|
simpr |
|
18 |
|
opeq2 |
|
19 |
|
simpr |
|
20 |
|
opex |
|
21 |
20
|
a1i |
|
22 |
10 18 19 21
|
fvmptd3 |
|
23 |
22
|
3adant2 |
|
24 |
23
|
adantr |
|
25 |
16 17 24
|
3eqtrd |
|
26 |
|
vex |
|
27 |
26
|
a1i |
|
28 |
|
opthg2 |
|
29 |
1 27 28
|
syl2anc |
|
30 |
29
|
simplbda |
|
31 |
12 25 30
|
syl2anc |
|
32 |
31
|
ex |
|
33 |
32
|
3expb |
|
34 |
33
|
ralrimivva |
|
35 |
|
dff13 |
|
36 |
11 34 35
|
sylanbrc |
|
37 |
|
elsnxp |
|
38 |
1 37
|
syl |
|
39 |
38
|
biimpa |
|
40 |
13
|
adantr |
|
41 |
|
id |
|
42 |
41
|
eqcomd |
|
43 |
42
|
adantl |
|
44 |
40 43
|
eqtr2d |
|
45 |
44
|
ex |
|
46 |
45
|
adantlr |
|
47 |
46
|
reximdva |
|
48 |
39 47
|
mpd |
|
49 |
48
|
ralrimiva |
|
50 |
|
dffo3 |
|
51 |
11 49 50
|
sylanbrc |
|
52 |
|
df-f1o |
|
53 |
36 51 52
|
sylanbrc |
|