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Theorem bd0 12949
Description: A formula equivalent to a bounded one is bounded. See also bd0r 12950. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0.min BOUNDED 𝜑
bd0.maj (𝜑𝜓)
Assertion
Ref Expression
bd0 BOUNDED 𝜓

Proof of Theorem bd0
StepHypRef Expression
1 bd0.min . 2 BOUNDED 𝜑
2 bd0.maj . . 3 (𝜑𝜓)
32ax-bd0 12938 . 2 (BOUNDED 𝜑BOUNDED 𝜓)
41, 3ax-mp 5 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 104  BOUNDED wbd 12937
This theorem was proved from axioms:  ax-mp 5  ax-bd0 12938
This theorem is referenced by:  bd0r  12950  bdth  12956  bdnth  12959  bdnthALT  12960  bdph  12975  bdsbc  12983  bdsnss  12998  bdcint  13002  bdeqsuc  13006  bdcriota  13008  bj-axun2  13040
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