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Theorem cdeqri 3754
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 3752 . 2 (CondEq(𝑥 = 𝑦𝜑) ↔ (𝑥 = 𝑦𝜑))
31, 2mpbi 231 1 (𝑥 = 𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  CondEqwcdeq 3751
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 3752
This theorem is referenced by:  cdeqnot  3756  cdeqal  3757  cdeqab  3758  cdeqal1  3759  cdeqab1  3760  cdeqim  3761  cdeqeq  3763  cdeqel  3764  nfcdeq  3765
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