Theorem bj-sbime 13808

Description: A strengthening of sbie 1784 (same proof). (Contributed by BJ, 16-Dec-2019.)

Hypotheses

Ref	Expression
bj-sbime.nf	|- F/ x ps
bj-sbime.1	|- ( x = y -> ( ph -> ps ) )

Assertion

Ref	Expression
bj-sbime	|- ( [ y / x ] ph -> ps )

Proof of Theorem bj-sbime

Step	Hyp	Ref	Expression
1		bj-sbime.nf	. . 3 |- F/ x ps
2	1	nfri 1512	. 2 |- ( ps -> A. x ps )
3		bj-sbime.1	. 2 |- ( x = y -> ( ph -> ps ) )
4	2, 3	bj-sbimeh 13807	1 |- ( [ y / x ] ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1453   [wsb 1755

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756

This theorem is referenced by:  setindis  14002  bdsetindis  14004