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	$$⊢A\in \mathrm{V}$$
Assertion	sbexi	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\exists x\phi \leftrightarrow \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		sbexi.1	$$⊢A\in \mathrm{V}$$
2		nfe1	$$⊢Ⅎx\exists x\phi$$
3	1 2	sbcgfi	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\exists x\phi \leftrightarrow \exists x\phi$$