Step |
Hyp |
Ref |
Expression |
1 |
|
remulcan2d.1 |
|
2 |
|
remulcan2d.2 |
|
3 |
|
remulcan2d.3 |
|
4 |
|
remulcan2d.4 |
|
5 |
|
ax-rrecex |
|
6 |
3 4 5
|
syl2anc |
|
7 |
|
oveq1 |
|
8 |
1
|
adantr |
|
9 |
8
|
recnd |
|
10 |
3
|
adantr |
|
11 |
10
|
recnd |
|
12 |
|
simprl |
|
13 |
12
|
recnd |
|
14 |
9 11 13
|
mulassd |
|
15 |
|
simprr |
|
16 |
15
|
oveq2d |
|
17 |
|
ax-1rid |
|
18 |
8 17
|
syl |
|
19 |
14 16 18
|
3eqtrd |
|
20 |
2
|
adantr |
|
21 |
20
|
recnd |
|
22 |
21 11 13
|
mulassd |
|
23 |
15
|
oveq2d |
|
24 |
|
ax-1rid |
|
25 |
20 24
|
syl |
|
26 |
22 23 25
|
3eqtrd |
|
27 |
19 26
|
eqeq12d |
|
28 |
7 27
|
syl5ib |
|
29 |
6 28
|
rexlimddv |
|
30 |
|
oveq1 |
|
31 |
29 30
|
impbid1 |
|