Step |
Hyp |
Ref |
Expression |
1 |
|
brprop.a |
|
2 |
|
brprop.b |
|
3 |
|
brprop.c |
|
4 |
|
brprop.d |
|
5 |
|
mptprop.1 |
|
6 |
|
df-pr |
|
7 |
|
fmptsn |
|
8 |
1 2 7
|
syl2anc |
|
9 |
|
incom |
|
10 |
|
prid1g |
|
11 |
|
snssi |
|
12 |
1 10 11
|
3syl |
|
13 |
|
df-ss |
|
14 |
12 13
|
sylib |
|
15 |
9 14
|
eqtr3id |
|
16 |
15
|
mpteq1d |
|
17 |
8 16
|
eqtr4d |
|
18 |
|
fmptsn |
|
19 |
3 4 18
|
syl2anc |
|
20 |
|
difprsn1 |
|
21 |
5 20
|
syl |
|
22 |
21
|
mpteq1d |
|
23 |
19 22
|
eqtr4d |
|
24 |
17 23
|
uneq12d |
|
25 |
|
partfun |
|
26 |
24 25
|
eqtr4di |
|
27 |
|
elsn2g |
|
28 |
1 27
|
syl |
|
29 |
28
|
ifbid |
|
30 |
29
|
mpteq2dv |
|
31 |
26 30
|
eqtrd |
|
32 |
6 31
|
syl5eq |
|