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Theorem bd0 9259
Description: A formula equivalent to a bounded one is bounded. See also bd0r 9260. (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 9248 . 2 (BOUNDED φBOUNDED ψ)
41, 3ax-mp 7 1 BOUNDED ψ
Colors of variables: wff set class
Syntax hints:  wb 98  BOUNDED wbd 9247
This theorem was proved from axioms:  ax-mp 7  ax-bd0 9248
This theorem is referenced by:  bd0r  9260  bdth  9266  bdnth  9269  bdnthALT  9270  bdph  9285  bdsbc  9293  bdsnss  9308  bdcint  9312  bdeqsuc  9316  bdcriota  9318  bj-axun2  9346
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