Theorem sbcgfi

Description: Substitution for a variable not free in a wff does not affect it, in inference form. (Contributed by Giovanni Mascellani, 1-Jun-2019)

	Ref	Expression
Hypotheses	sbcgfi.1	|- A e. _V
	sbcgfi.2	|- F/ x ph
Assertion	sbcgfi	|- ( [. A / x ]. ph <-> ph )

Proof

Step	Hyp	Ref	Expression
1		sbcgfi.1	|- A e. _V
2		sbcgfi.2	|- F/ x ph
3	2	sbcgf	|- ( A e. _V -> ( [. A / x ]. ph <-> ph ) )
4	1 3	ax-mp	|- ( [. A / x ]. ph <-> ph )