ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cdeqth GIF version

Theorem cdeqth 2811
Description: Deduce conditional equality from a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqth.1 𝜑
Assertion
Ref Expression
cdeqth CondEq(𝑥 = 𝑦𝜑)

Proof of Theorem cdeqth
StepHypRef Expression
1 cdeqth.1 . . 3 𝜑
21a1i 9 . 2 (𝑥 = 𝑦𝜑)
32cdeqi 2809 1 CondEq(𝑥 = 𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  CondEqwcdeq 2807
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-cdeq 2808
This theorem is referenced by:  cdeqal1  2815  cdeqab1  2816  nfccdeq  2822
  Copyright terms: Public domain W3C validator