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Theorem bdeq 10799
Description: Equality property for the predicate BOUNDED. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeq.1 (𝜑𝜓)
Assertion
Ref Expression
bdeq (BOUNDED 𝜑BOUNDED 𝜓)

Proof of Theorem bdeq
StepHypRef Expression
1 bdeq.1 . . 3 (𝜑𝜓)
21ax-bd0 10789 . 2 (BOUNDED 𝜑BOUNDED 𝜓)
31bicomi 130 . . 3 (𝜓𝜑)
43ax-bd0 10789 . 2 (BOUNDED 𝜓BOUNDED 𝜑)
52, 4impbii 124 1 (BOUNDED 𝜑BOUNDED 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 103  BOUNDED wbd 10788
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 10789
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bdceq  10818
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