Theorem equsb1vOLDOLD

Description: Obsolete version of equsb1v as of 19-Jun-2023. (Contributed by BJ, 11-Sep-2019) Remove dependencies on axioms. (Revised by Wolf Lammen, 30-May-2023) (Proof shortened by Steven Nguyen, 31-May-2023) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	equsb1vOLDOLD	$$⊢\left[y/x\right]x=y$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢x=y\to x=y$$
2		ax6ev	$$⊢\exists xx=y$$
3	1	ancli	$$⊢x=y\to \left(x=y\wedge x=y\right)$$
4	2 3	eximii	$$⊢\exists x\left(x=y\wedge x=y\right)$$
5		dfsb1	$$⊢\left[y/x\right]x=y\leftrightarrow \left(\left(x=y\to x=y\right)\wedge \exists x\left(x=y\wedge x=y\right)\right)$$
6	1 4 5	mpbir2an	$$⊢\left[y/x\right]x=y$$