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

Theorem cdeqcv 2985
Description: Conditional equality for set-to-class promotion. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
cdeqcv  |- CondEq ( x  =  y  ->  x  =  y )

Proof of Theorem cdeqcv
StepHypRef Expression
1 id 19 . 2  |-  ( x  =  y  ->  x  =  y )
21cdeqi 2976 1  |- CondEq ( x  =  y  ->  x  =  y )
Colors of variables: wff set class
Syntax hints:    = wceq 1623  CondEqwcdeq 2974
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 177  df-cdeq 2975
  Copyright terms: Public domain W3C validator