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Mirrors > Home > MPE Home > Th. List > cdeqth | Structured version Visualization version GIF version |
Description: Deduce conditional equality from a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
cdeqth.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
cdeqth | ⊢ CondEq(𝑥 = 𝑦 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdeqth.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | a1i 11 | . 2 ⊢ (𝑥 = 𝑦 → 𝜑) |
3 | 2 | cdeqi 3678 | 1 ⊢ CondEq(𝑥 = 𝑦 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: CondEqwcdeq 3676 |
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 210 df-cdeq 3677 |
This theorem is referenced by: cdeqal1 3684 cdeqab1 3685 nfccdeq 3691 |
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