Step |
Hyp |
Ref |
Expression |
1 |
|
simp1 |
|
2 |
|
simp2 |
|
3 |
|
simp1 |
|
4 |
|
funcnvpr |
|
5 |
1 2 3 4
|
syl2an3an |
|
6 |
|
funcnvsn |
|
7 |
6
|
a1i |
|
8 |
|
df-rn |
|
9 |
|
rnpropg |
|
10 |
8 9
|
syl5eqr |
|
11 |
10
|
3adant3 |
|
12 |
|
df-rn |
|
13 |
|
rnsnopg |
|
14 |
12 13
|
syl5eqr |
|
15 |
14
|
3ad2ant3 |
|
16 |
11 15
|
ineq12d |
|
17 |
|
disjprsn |
|
18 |
17
|
3adant1 |
|
19 |
16 18
|
sylan9eq |
|
20 |
|
funun |
|
21 |
5 7 19 20
|
syl21anc |
|
22 |
|
df-tp |
|
23 |
22
|
cnveqi |
|
24 |
|
cnvun |
|
25 |
23 24
|
eqtri |
|
26 |
25
|
funeqi |
|
27 |
21 26
|
sylibr |
|