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Mirrors > Home > ILE Home > Th. List > clel4 | Unicode version |
Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
clel4.1 |
Ref | Expression |
---|---|
clel4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clel4.1 | . . 3 | |
2 | eleq2 2234 | . . 3 | |
3 | 1, 2 | ceqsalv 2760 | . 2 |
4 | 3 | bicomi 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1346 wceq 1348 wcel 2141 cvv 2730 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: intpr 3863 |
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