Theorem sbcim1OLD

Description: Obsolete version of sbcim1 as of 26-Oct-2024. (Contributed by NM, 17-Aug-2018) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sbcim1OLD	|- ( [. A / x ]. ( ph -> ps ) -> ( [. A / x ]. ph -> [. A / x ]. ps ) )

Proof

Step	Hyp	Ref	Expression
1		sbcex	|- ( [. A / x ]. ( ph -> ps ) -> A e. _V )
2		sbcimg	|- ( A e. _V -> ( [. A / x ]. ( ph -> ps ) <-> ( [. A / x ]. ph -> [. A / x ]. ps ) ) )
3	2	biimpd	|- ( A e. _V -> ( [. A / x ]. ( ph -> ps ) -> ( [. A / x ]. ph -> [. A / x ]. ps ) ) )
4	1 3	mpcom	|- ( [. A / x ]. ( ph -> ps ) -> ( [. A / x ]. ph -> [. A / x ]. ps ) )