Theorem sbexi

Description: Discard class substitution in an existential quantification when substituting the quantified variable, in inference form. (Contributed by Giovanni Mascellani, 27-May-2019)

	Ref	Expression
Hypothesis	sbexi.1	|- A e. _V
Assertion	sbexi	|- ( [. A / x ]. E. x ph <-> E. x ph )

Proof

Step	Hyp	Ref	Expression
1		sbexi.1	|- A e. _V
2		nfe1	|- F/ x E. x ph
3	1 2	sbcgfi	|- ( [. A / x ]. E. x ph <-> E. x ph )