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Mirrors > Home > MPE Home > Th. List > cdeqcv | Structured version Visualization version 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 22 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
2 | 1 | cdeqi 3691 | 1 ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: CondEqwcdeq 3689 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 208 df-cdeq 3690 |
This theorem is referenced by: (None) |
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