MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  cdeqth Structured version   Unicode version

Theorem cdeqth 3148
Description: Deduce conditional equality from a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqth.1  |-  ph
Assertion
Ref Expression
cdeqth  |- CondEq ( x  =  y  ->  ph )

Proof of Theorem cdeqth
StepHypRef Expression
1 cdeqth.1 . . 3  |-  ph
21a1i 11 . 2  |-  ( x  =  y  ->  ph )
32cdeqi 3146 1  |- CondEq ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:  CondEqwcdeq 3144
This theorem is referenced by:  cdeqal1  3152  cdeqab1  3153  nfccdeq  3159
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-cdeq 3145
  Copyright terms: Public domain W3C validator