Theorem sbiedwOLD

Description: Obsolete version of sbiedw as of 28-Jan-2024. (Contributed by Gino Giotto, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	sbiedw.1	|- F/ x ph
	sbiedw.2	|- ( ph -> F/ x ch )
	sbiedw.3	|- ( ph -> ( x = y -> ( ps <-> ch ) ) )
Assertion	sbiedwOLD	|- ( ph -> ( [ y / x ] ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		sbiedw.1	|- F/ x ph
2		sbiedw.2	|- ( ph -> F/ x ch )
3		sbiedw.3	|- ( ph -> ( x = y -> ( ps <-> ch ) ) )
4	1	sbrim	|- ( [ y / x ] ( ph -> ps ) <-> ( ph -> [ y / x ] ps ) )
5	1 2	nfim1	|- F/ x ( ph -> ch )
6	3	com12	|- ( x = y -> ( ph -> ( ps <-> ch ) ) )
7	6	pm5.74d	|- ( x = y -> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
8	5 7	sbiev	|- ( [ y / x ] ( ph -> ps ) <-> ( ph -> ch ) )
9	4 8	bitr3i	|- ( ( ph -> [ y / x ] ps ) <-> ( ph -> ch ) )
10	9	pm5.74ri	|- ( ph -> ( [ y / x ] ps <-> ch ) )