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Theorem cdeqri 2802
Description: Property of conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqri.1 CondEq(𝑥 = 𝑦𝜑)
Assertion
Ref Expression
cdeqri (𝑥 = 𝑦𝜑)

Proof of Theorem cdeqri
StepHypRef Expression
1 cdeqri.1 . 2 CondEq(𝑥 = 𝑦𝜑)
2 df-cdeq 2800 . 2 (CondEq(𝑥 = 𝑦𝜑) ↔ (𝑥 = 𝑦𝜑))
31, 2mpbi 143 1 (𝑥 = 𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  CondEqwcdeq 2799
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-cdeq 2800
This theorem is referenced by:  cdeqnot  2804  cdeqal  2805  cdeqab  2806  cdeqal1  2807  cdeqab1  2808  cdeqim  2809  cdeqeq  2811  cdeqel  2812  nfcdeq  2813
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