Theorem bj-sbime 14765

Description: A strengthening of sbie 1801 (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 1529	. 2 |- ( ps -> A. x ps )
3		bj-sbime.1	. 2 |- ( x = y -> ( ph -> ps ) )
4	2, 3	bj-sbimeh 14764	1 |- ( [ y / x ] ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1470   [wsb 1772

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773

This theorem is referenced by:  setindis  14959  bdsetindis  14961