Theorem sb2vOLD

Description: Obsolete as of 30-Jul-2023. Use sb6 instead. Version of sb2 with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 31-May-2019) Revise df-sb . (Revised by Steven Nguyen, 8-Jul-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb2vOLD	$$⊢\forall x\left(x=y\to \phi \right)\to \left[y/x\right]\phi$$

Proof

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