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Theorem bd0 10331
Description: A formula equivalent to a bounded one is bounded. See also bd0r 10332. (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 10320 . 2 (BOUNDED 𝜑BOUNDED 𝜓)
41, 3ax-mp 7 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 102  BOUNDED wbd 10319
This theorem was proved from axioms:  ax-mp 7  ax-bd0 10320
This theorem is referenced by:  bd0r  10332  bdth  10338  bdnth  10341  bdnthALT  10342  bdph  10357  bdsbc  10365  bdsnss  10380  bdcint  10384  bdeqsuc  10388  bdcriota  10390  bj-axun2  10422
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