Theorem sbali

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

	Ref	Expression
Hypothesis	sbali.1	$$⊢A\in \mathrm{V}$$
Assertion	sbali	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\forall x\phi \leftrightarrow \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		sbali.1	$$⊢A\in \mathrm{V}$$
2		nfa1	$$⊢Ⅎx\forall x\phi$$
3	1 2	sbcgfi	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\forall x\phi \leftrightarrow \forall x\phi$$