Theorem nfsbvOLD

Description: Obsolete version of nfsbv as of 13-Aug-2023. (Contributed by Wolf Lammen, 7-Feb-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nfsbv.nf	$$⊢Ⅎz\phi$$
Assertion	nfsbvOLD	$$⊢Ⅎz\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfsbv.nf	$$⊢Ⅎz\phi$$
2		sb6	$$⊢\left[y/x\right]\phi \leftrightarrow \forall x\left(x=y\to \phi \right)$$
3		nfv	$$⊢Ⅎzx=y$$
4	3 1	nfim	$$⊢Ⅎz\left(x=y\to \phi \right)$$
5	4	nfal	$$⊢Ⅎz\forall x\left(x=y\to \phi \right)$$
6	2 5	nfxfr	$$⊢Ⅎz\left[y/x\right]\phi$$