Theorem nfs1v

Description: The setvar x is not free in [ y / x ] ph when x and y are distinct. (Contributed by Mario Carneiro, 11-Aug-2016) Shorten nfs1v and hbs1 combined. (Revised by Wolf Lammen, 28-Jul-2022)

	Ref	Expression
Assertion	nfs1v	$$⊢Ⅎx\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		sb6	$$⊢\left[y/x\right]\phi \leftrightarrow \forall x\left(x=y\to \phi \right)$$
2		nfa1	$$⊢Ⅎx\forall x\left(x=y\to \phi \right)$$
3	1 2	nfxfr	$$⊢Ⅎx\left[y/x\right]\phi$$