Theorem bd0 16850

Description: A formula equivalent to a bounded one is bounded. See also bd0r 16851. (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 16839	. 2 |- (BOUNDED ph -> BOUNDED ps )
4	1, 3	ax-mp 5	1 |- BOUNDED ps

This proof depends on syntax axioms:   <-> wb 105  BOUNDED wbd 16838

This proof depends on axioms:  ax-mp 5  ax-bd0 16839

This theorem is used by:  bd0r  16851  bdth  16857  bdnth  16860  bdnthALT  16861  bdph  16876  bdsbc  16884  bdsnss  16899  bdcint  16903  bdeqsuc  16907  bdcriota  16909  bj-axun2  16941