Theorem bj-sbime 15746

Description: A strengthening of sbie 1814 (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 1542	. 2 |- ( ps -> A. x ps )
3		bj-sbime.1	. 2 |- ( x = y -> ( ph -> ps ) )
4	2, 3	bj-sbimeh 15745	1 |- ( [ y / x ] ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1483   [wsb 1785

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-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786

This theorem is referenced by:  setindis  15940  bdsetindis  15942