Theorem bd0 15959

Description: A formula equivalent to a bounded one is bounded. See also bd0r 15960. (Contributed by BJ, 3-Oct-2019.)

Hypotheses

Ref	Expression
bd0.min	|- BOUNDED ph
bd0.maj	|- ( ph <-> ps )

Assertion

Ref	Expression
bd0	|- BOUNDED ps

Proof of Theorem bd0

Step	Hyp	Ref	Expression
1		bd0.min	. 2 |- BOUNDED ph
2		bd0.maj	. . 3 |- ( ph <-> ps )
3	2	ax-bd0 15948	. 2 |- (BOUNDED ph -> BOUNDED ps )
4	1, 3	ax-mp 5	1 |- BOUNDED ps

Syntax hints:   <-> wb 105  BOUNDED wbd 15947

This theorem was proved from axioms:  ax-mp 5  ax-bd0 15948

This theorem is referenced by:  bd0r  15960  bdth  15966  bdnth  15969  bdnthALT  15970  bdph  15985  bdsbc  15993  bdsnss  16008  bdcint  16012  bdeqsuc  16016  bdcriota  16018  bj-axun2  16050