Theorem nfa1w

Description: Replace ax-10 in nfa1 with a substitution hypothesis. (Contributed by SN, 2-Sep-2025)

	Ref	Expression
Hypothesis	nfa1w.x	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	nfa1w	$$⊢Ⅎx\forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfa1w.x	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2	1	cbvalvw	$$⊢\forall x\phi \leftrightarrow \forall y\psi$$
3		nfv	$$⊢Ⅎx\forall y\psi$$
4	2 3	nfxfr	$$⊢Ⅎx\forall x\phi$$