Theorem bd0 9944

Description: A formula equivalent to a bounded one is bounded. See also bd0r 9945. (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 9933	. 2 |- (BOUNDED ph -> BOUNDED ps )
4	1, 3	ax-mp 7	1 |- BOUNDED ps

Syntax hints:   <-> wb 98  BOUNDED wbd 9932

This theorem was proved from axioms:  ax-mp 7  ax-bd0 9933

This theorem is referenced by:  bd0r  9945  bdth  9951  bdnth  9954  bdnthALT  9955  bdph  9970  bdsbc  9978  bdsnss  9993  bdcint  9997  bdeqsuc  10001  bdcriota  10003  bj-axun2  10035