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Mirrors > Home > ILE Home > Th. List > cdeqel | Unicode version |
Description: Distribute conditional equality over elementhood. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
cdeqeq.1 | CondEq |
cdeqeq.2 | CondEq |
Ref | Expression |
---|---|
cdeqel | CondEq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdeqeq.1 | . . . 4 CondEq | |
2 | 1 | cdeqri 2801 | . . 3 |
3 | cdeqeq.2 | . . . 4 CondEq | |
4 | 3 | cdeqri 2801 | . . 3 |
5 | 2, 4 | eleq12d 2149 | . 2 |
6 | 5 | cdeqi 2800 | 1 CondEq |
Colors of variables: wff set class |
Syntax hints: wb 103 wceq 1284 wcel 1433 CondEqwcdeq 2798 |
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 df-cdeq 2799 |
This theorem is referenced by: nfccdeq 2813 |
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