Theorem sbievOLD

Description: Obsolete proof of sbiev as of 18-Jul-2023. (Contributed by Wolf Lammen, 18-Jan-2023) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	sbiev.1	|- F/ x ps
	sbiev.2	|- ( x = y -> ( ph <-> ps ) )
Assertion	sbievOLD	|- ( [ y / x ] ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		sbiev.1	|- F/ x ps
2		sbiev.2	|- ( x = y -> ( ph <-> ps ) )
3		equsb1v	|- [ y / x ] x = y
4	2	sbimi	|- ( [ y / x ] x = y -> [ y / x ] ( ph <-> ps ) )
5	3 4	ax-mp	|- [ y / x ] ( ph <-> ps )
6	1	sbf	|- ( [ y / x ] ps <-> ps )
7	6	sblbisvOLD	|- ( [ y / x ] ( ph <-> ps ) <-> ( [ y / x ] ph <-> ps ) )
8	5 7	mpbi	|- ( [ y / x ] ph <-> ps )