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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 |
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cdeqeq.2 |
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Ref | Expression |
---|---|
cdeqel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdeqeq.1 |
. . . 4
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2 | 1 | cdeqri 2814 |
. . 3
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3 | cdeqeq.2 |
. . . 4
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4 | 3 | cdeqri 2814 |
. . 3
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5 | 2, 4 | eleq12d 2155 |
. 2
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6 | 5 | cdeqi 2813 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 1379 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-4 1443 ax-17 1462 ax-ial 1470 ax-ext 2067 |
This theorem depends on definitions: df-bi 115 df-cleq 2078 df-clel 2081 df-cdeq 2812 |
This theorem is referenced by: nfccdeq 2826 |
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