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

Theorem cdeqri 2750
Description: Property of conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqri.1  |- CondEq ( x  =  y  ->  ph )
Assertion
Ref Expression
cdeqri  |-  ( x  =  y  ->  ph )

Proof of Theorem cdeqri
StepHypRef Expression
1 cdeqri.1 . 2  |- CondEq ( x  =  y  ->  ph )
2 df-cdeq 2748 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
31, 2mpbi 133 1  |-  ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2747
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-cdeq 2748
This theorem is referenced by:  cdeqnot  2752  cdeqal  2753  cdeqab  2754  cdeqal1  2755  cdeqab1  2756  cdeqim  2757  cdeqeq  2759  cdeqel  2760  nfcdeq  2761
  Copyright terms: Public domain W3C validator