Description: A version of mulc1cncf using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Glauco Siliprandi, 30-Jun-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mulc1cncfg.1 | |
|
mulc1cncfg.2 | |
||
mulc1cncfg.3 | |
||
mulc1cncfg.4 | |
||
Assertion | mulc1cncfg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mulc1cncfg.1 | |
|
2 | mulc1cncfg.2 | |
|
3 | mulc1cncfg.3 | |
|
4 | mulc1cncfg.4 | |
|
5 | eqid | |
|
6 | 5 | mulc1cncf | |
7 | 4 6 | syl | |
8 | cncff | |
|
9 | 7 8 | syl | |
10 | cncff | |
|
11 | 3 10 | syl | |
12 | fcompt | |
|
13 | 9 11 12 | syl2anc | |
14 | 11 | ffvelrnda | |
15 | 4 | adantr | |
16 | 15 14 | mulcld | |
17 | nfcv | |
|
18 | 1 17 | nffv | |
19 | nfcv | |
|
20 | nfcv | |
|
21 | 19 20 18 | nfov | |
22 | oveq2 | |
|
23 | 18 21 22 5 | fvmptf | |
24 | 14 16 23 | syl2anc | |
25 | 24 | mpteq2dva | |
26 | nfcv | |
|
27 | nfcv | |
|
28 | nfcv | |
|
29 | 26 27 28 | nfov | |
30 | fveq2 | |
|
31 | 30 | oveq2d | |
32 | 21 29 31 | cbvmpt | |
33 | 25 32 | eqtrdi | |
34 | 13 33 | eqtrd | |
35 | 3 7 | cncfco | |
36 | 34 35 | eqeltrrd | |