Theorem sb4vOLDOLD

Description: Obsolete version of sb4vOLD as of 8-Jul-2023. Version of sb4OLD with a disjoint variable condition instead of a distinctor antecedent, which does not require ax-13 . (Contributed by BJ, 23-Jun-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb4vOLDOLD	$$⊢\left[y/x\right]\phi \to \forall x\left(x=y\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sb1	$$⊢\left[y/x\right]\phi \to \exists x\left(x=y\wedge \phi \right)$$
2		sb56	$$⊢\exists x\left(x=y\wedge \phi \right)\leftrightarrow \forall x\left(x=y\to \phi \right)$$
3	1 2	sylib	$$⊢\left[y/x\right]\phi \to \forall x\left(x=y\to \phi \right)$$