Theorem bdsbcALT 16180

Description: Alternate proof of bdsbc 16179. (Contributed by BJ, 16-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bdcsbc.1	|- BOUNDED ph

Assertion

Ref	Expression
bdsbcALT	|- BOUNDED [. y / x ]. ph

Proof of Theorem bdsbcALT

Step	Hyp	Ref	Expression
1		bdcsbc.1	. . 3 |- BOUNDED ph
2	1	bdab 16159	. 2 |- BOUNDED y e. { x | ph }
3		df-sbc 3029	. 2 |- ( [. y / x ]. ph <-> y e. { x | ph } )
4	2, 3	bd0r 16146	1 |- BOUNDED [. y / x ]. ph

Syntax hints:   e. wcel 2200   {cab 2215   [.wsbc 3028  BOUNDED wbd 16133

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 16134  ax-bdsb 16143

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-sbc 3029

This theorem is referenced by: (None)