Metamath Proof Explorer


Theorem sbievwOLD

Description: Obsolete version of sbievw as of 24-Aug-2025. (Contributed by NM, 30-Jun-1994) (Revised by BJ, 18-Jul-2023) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step Hyp Ref Expression
1 sbievw.is
 |-  ( x = y -> ( ph <-> ps ) )
2 sb6
 |-  ( [ y / x ] ph <-> A. x ( x = y -> ph ) )
3 1 equsalvw
 |-  ( A. x ( x = y -> ph ) <-> ps )
4 2 3 bitri
 |-  ( [ y / x ] ph <-> ps )