Theorem equsb1vOLD

Description: Obsolete version of equsb1v as of 22-Jul-2023. Version of equsb1 with a disjoint variable condition, which neither requires ax-12 nor ax-13 . (Contributed by BJ, 11-Sep-2019) Remove dependencies on axioms. (Revised by Wolf Lammen, 30-May-2023) (Proof shortened by Steven Nguyen, 19-Jun-2023) Revise df-sb . (Revised by Steven Nguyen, 11-Jul-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	equsb1vOLD	$$⊢\left[y/x\right]x=y$$

Proof

Step	Hyp	Ref	Expression
1		sb2vOLD	$$⊢\forall x\left(x=y\to x=y\right)\to \left[y/x\right]x=y$$
2		id	$$⊢x=y\to x=y$$
3	1 2	mpg	$$⊢\left[y/x\right]x=y$$