Theorem bd0 16470

Description: A formula equivalent to a bounded one is bounded. See also bd0r 16471. (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 16459	. 2 |- (BOUNDED ph -> BOUNDED ps )
4	1, 3	ax-mp 5	1 |- BOUNDED ps

Syntax hints:   <-> wb 105  BOUNDED wbd 16458

This theorem was proved from axioms:  ax-mp 5  ax-bd0 16459

This theorem is referenced by:  bd0r  16471  bdth  16477  bdnth  16480  bdnthALT  16481  bdph  16496  bdsbc  16504  bdsnss  16519  bdcint  16523  bdeqsuc  16527  bdcriota  16529  bj-axun2  16561