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Theorem bdcdeq 11073
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 11054 . . 3  |- BOUNDED  x  =  y
2 bdcdeq.1 . . 3  |- BOUNDED  ph
31, 2ax-bdim 11048 . 2  |- BOUNDED  ( x  =  y  ->  ph )
4 df-cdeq 2810 . 2  |-  (CondEq (
x  =  y  ->  ph )  <->  ( x  =  y  ->  ph ) )
53, 4bd0r 11059 1  |- BOUNDED CondEq ( x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4  CondEqwcdeq 2809  BOUNDED wbd 11046
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11047  ax-bdim 11048  ax-bdeq 11054
This theorem depends on definitions:  df-bi 115  df-cdeq 2810
This theorem is referenced by: (None)
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