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Theorem bdeq 13598
Description: Equality property for the predicate BOUNDED. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeq.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
bdeq  |-  (BOUNDED  ph  <-> BOUNDED  ps )

Proof of Theorem bdeq
StepHypRef Expression
1 bdeq.1 . . 3  |-  ( ph  <->  ps )
21ax-bd0 13588 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
31bicomi 131 . . 3  |-  ( ps  <->  ph )
43ax-bd0 13588 . 2  |-  (BOUNDED  ps  -> BOUNDED  ph )
52, 4impbii 125 1  |-  (BOUNDED  ph  <-> BOUNDED  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104  BOUNDED wbd 13587
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 13588
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bdceq  13617
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