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Mirrors > Home > ILE Home > Th. List > cdeqth | 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 9 | . 2 ⊢ (𝑥 = 𝑦 → 𝜑) |
3 | 2 | cdeqi 2949 | 1 ⊢ CondEq(𝑥 = 𝑦 → 𝜑) |
Colors of variables: wff set class |
Syntax hints: CondEqwcdeq 2947 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-cdeq 2948 |
This theorem is referenced by: cdeqal1 2955 cdeqab1 2956 nfccdeq 2962 |
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