Description: Lemma 1 for rhmsubc . (Contributed by AV, 2-Mar-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | rngcrescrhm.u | |
|
rngcrescrhm.c | |
||
rngcrescrhm.r | |
||
rngcrescrhm.h | |
||
Assertion | rhmsubclem1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rngcrescrhm.u | |
|
2 | rngcrescrhm.c | |
|
3 | rngcrescrhm.r | |
|
4 | rngcrescrhm.h | |
|
5 | eqid | |
|
6 | ovex | |
|
7 | 6 | inex1 | |
8 | 5 7 | fnmpoi | |
9 | 4 | a1i | |
10 | dfrhm2 | |
|
11 | 10 | a1i | |
12 | 11 | reseq1d | |
13 | inss1 | |
|
14 | 3 13 | eqsstrdi | |
15 | resmpo | |
|
16 | 14 14 15 | syl2anc | |
17 | 9 12 16 | 3eqtrd | |
18 | 17 | fneq1d | |
19 | 8 18 | mpbiri | |