Description: Sufficient condition for elementhood in the set M . (Contributed by Mario Carneiro, 16-Mar-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | elovolm.1 | |
|
elovolmr.2 | |
||
Assertion | elovolmr | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elovolm.1 | |
|
2 | elovolmr.2 | |
|
3 | elovolmlem | |
|
4 | id | |
|
5 | 4 | eqcomd | |
6 | 5 | coeq2d | |
7 | 6 | seqeq3d | |
8 | 2 7 | eqtrid | |
9 | 8 | rneqd | |
10 | 9 | supeq1d | |
11 | 10 | biantrud | |
12 | coeq2 | |
|
13 | 12 | rneqd | |
14 | 13 | unieqd | |
15 | 14 | sseq2d | |
16 | 11 15 | bitr3d | |
17 | 16 | rspcev | |
18 | 3 17 | sylanbr | |
19 | 1 | elovolm | |
20 | 18 19 | sylibr | |