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Mirrors > Home > ILE Home > Th. List > syl5eleq | Unicode version |
Description: B membership and equality inference. (Contributed by NM, 4-Jan-2006.) |
Ref | Expression |
---|---|
syl5eleq.1 | |
syl5eleq.2 |
Ref | Expression |
---|---|
syl5eleq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eleq.1 | . . 3 | |
2 | 1 | a1i 9 | . 2 |
3 | syl5eleq.2 | . 2 | |
4 | 2, 3 | eleqtrd 2116 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: syl5eleqr 2127 opth1 3973 opth 3974 eqelsuc 4156 bj-nnelirr 10078 |
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