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Theorem bdeq 10330
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 10320 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
31bicomi 127 . . 3  |-  ( ps  <->  ph )
43ax-bd0 10320 . 2  |-  (BOUNDED  ps  -> BOUNDED  ph )
52, 4impbii 121 1  |-  (BOUNDED  ph  <-> BOUNDED  ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 102  BOUNDED wbd 10319
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-bd0 10320
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  bdceq  10349
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