Theorem sbievw

Description: Conversion of implicit substitution to explicit substitution. Version of sbie and sbiev with more disjoint variable conditions, requiring fewer axioms. (Contributed by NM, 30-Jun-1994) (Revised by BJ, 18-Jul-2023) (Proof shortened by SN, 24-Aug-2025)

	Ref	Expression
Hypothesis	sbievw.is	|- ( x = y -> ( ph <-> ps ) )
Assertion	sbievw	|- ( [ y / x ] ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		sbievw.is	|- ( x = y -> ( ph <-> ps ) )
2	1	sbbiiev	|- ( [ y / x ] ph <-> [ y / x ] ps )
3		sbv	|- ( [ y / x ] ps <-> ps )
4	2 3	bitri	|- ( [ y / x ] ph <-> ps )