Theorem sbrimvwOLD

Description: Obsolete version of sbrimvw as of 5-Jun-2026. (Contributed by Wolf Lammen, 29-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sbrimvwOLD	|- ( [ y / x ] ( ph -> ps ) <-> ( ph -> [ y / x ] ps ) )

Proof

Step	Hyp	Ref	Expression
1		sb6	|- ( [ y / x ] ( ph -> ps ) <-> A. x ( x = y -> ( ph -> ps ) ) )
2		bi2.04	|- ( ( ph -> ( x = y -> ps ) ) <-> ( x = y -> ( ph -> ps ) ) )
3	2	albii	|- ( A. x ( ph -> ( x = y -> ps ) ) <-> A. x ( x = y -> ( ph -> ps ) ) )
4		19.21v	|- ( A. x ( ph -> ( x = y -> ps ) ) <-> ( ph -> A. x ( x = y -> ps ) ) )
5	1 3 4	3bitr2i	|- ( [ y / x ] ( ph -> ps ) <-> ( ph -> A. x ( x = y -> ps ) ) )
6		sb6	|- ( [ y / x ] ps <-> A. x ( x = y -> ps ) )
7	6	imbi2i	|- ( ( ph -> [ y / x ] ps ) <-> ( ph -> A. x ( x = y -> ps ) ) )
8	5 7	bitr4i	|- ( [ y / x ] ( ph -> ps ) <-> ( ph -> [ y / x ] ps ) )