Step |
Hyp |
Ref |
Expression |
1 |
|
fucidcl.q |
|
2 |
|
fucidcl.n |
|
3 |
|
fucidcl.x |
|
4 |
|
fucidcl.f |
|
5 |
|
funcrcl |
|
6 |
4 5
|
syl |
|
7 |
6
|
simprd |
|
8 |
|
eqid |
|
9 |
8 3
|
cidfn |
|
10 |
7 9
|
syl |
|
11 |
|
dffn2 |
|
12 |
10 11
|
sylib |
|
13 |
|
eqid |
|
14 |
|
relfunc |
|
15 |
|
1st2ndbr |
|
16 |
14 4 15
|
sylancr |
|
17 |
13 8 16
|
funcf1 |
|
18 |
|
fcompt |
|
19 |
12 17 18
|
syl2anc |
|
20 |
|
eqid |
|
21 |
7
|
adantr |
|
22 |
17
|
ffvelrnda |
|
23 |
8 20 3 21 22
|
catidcl |
|
24 |
23
|
ralrimiva |
|
25 |
|
fvex |
|
26 |
|
mptelixpg |
|
27 |
25 26
|
ax-mp |
|
28 |
24 27
|
sylibr |
|
29 |
19 28
|
eqeltrd |
|
30 |
7
|
adantr |
|
31 |
|
simpr1 |
|
32 |
31 22
|
syldan |
|
33 |
|
eqid |
|
34 |
17
|
adantr |
|
35 |
|
simpr2 |
|
36 |
34 35
|
ffvelrnd |
|
37 |
|
eqid |
|
38 |
16
|
adantr |
|
39 |
13 37 20 38 31 35
|
funcf2 |
|
40 |
|
simpr3 |
|
41 |
39 40
|
ffvelrnd |
|
42 |
8 20 3 30 32 33 36 41
|
catlid |
|
43 |
8 20 3 30 32 33 36 41
|
catrid |
|
44 |
42 43
|
eqtr4d |
|
45 |
|
fvco3 |
|
46 |
34 35 45
|
syl2anc |
|
47 |
46
|
oveq1d |
|
48 |
|
fvco3 |
|
49 |
34 31 48
|
syl2anc |
|
50 |
49
|
oveq2d |
|
51 |
44 47 50
|
3eqtr4d |
|
52 |
51
|
ralrimivvva |
|
53 |
2 13 37 20 33 4 4
|
isnat2 |
|
54 |
29 52 53
|
mpbir2and |
|