Theorem bdsbcALT 9979

Description: Alternate proof of bdsbc 9978. (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 9958	. 2 |- BOUNDED y e. { x | ph }
3		df-sbc 2765	. 2 |- ( [. y / x ]. ph <-> y e. { x | ph } )
4	2, 3	bd0r 9945	1 |- BOUNDED [. y / x ]. ph

Syntax hints:   e. wcel 1393   {cab 2026   [.wsbc 2764  BOUNDED wbd 9932

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9933  ax-bdsb 9942

This theorem depends on definitions:  df-bi 110  df-clab 2027  df-sbc 2765

This theorem is referenced by: (None)