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Theorem bdcdeq 13022
Description: Conditional equality of a bounded formula is a bounded formula. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdcdeq.1  |- BOUNDED  ph
Assertion
Ref Expression
bdcdeq  |- BOUNDED CondEq ( x  =  y  ->  ph )

Proof of Theorem bdcdeq
StepHypRef Expression
1 ax-bdeq 13003 . . 3  |- BOUNDED  x  =  y
2 bdcdeq.1 . . 3  |- BOUNDED  ph
31, 2ax-bdim 12997 . 2  |- BOUNDED  ( x  =  y  ->  ph )
4 df-cdeq 2888 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
53, 4bd0r 13008 1  |- BOUNDED CondEq ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2887  BOUNDED wbd 12995
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-bd0 12996  ax-bdim 12997  ax-bdeq 13003
This theorem depends on definitions:  df-bi 116  df-cdeq 2888
This theorem is referenced by: (None)
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