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Mirrors > Home > ILE Home > Th. List > syl5eleqr | Unicode version |
Description: B membership and equality inference. (Contributed by NM, 4-Jan-2006.) |
Ref | Expression |
---|---|
syl5eleqr.1 | |
syl5eleqr.2 |
Ref | Expression |
---|---|
syl5eleqr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eleqr.1 | . 2 | |
2 | syl5eleqr.2 | . . 3 | |
3 | 2 | eqcomd 2086 | . 2 |
4 | 1, 3 | syl5eleq 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 df-clel 2077 |
This theorem is referenced by: rabsnt 3467 0elnn 4358 tfrexlem 5971 rdgtfr 5984 rdgruledefgg 5985 |
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