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Mirrors > Home > ILE Home > Th. List > cdeqcv | GIF version |
Description: Conditional equality for set-to-class promotion. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
cdeqcv | ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
2 | 1 | cdeqi 2814 | 1 ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦) |
Colors of variables: wff set class |
Syntax hints: CondEqwcdeq 2812 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-cdeq 2813 |
This theorem is referenced by: (None) |
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