Theorem sb5OLD

Description: Obsolete version of sb5 as of 21-Sep-2024. (Contributed by NM, 18-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb5OLD	$$⊢\left[y/x\right]\phi \leftrightarrow \exists x\left(x=y\wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfs1v	$$⊢Ⅎx\left[y/x\right]\phi$$
2		sbequ12	$$⊢x=y\to \left(\phi \leftrightarrow \left[y/x\right]\phi \right)$$
3	1 2	equsexv	$$⊢\exists x\left(x=y\wedge \phi \right)\leftrightarrow \left[y/x\right]\phi$$
4	3	bicomi	$$⊢\left[y/x\right]\phi \leftrightarrow \exists x\left(x=y\wedge \phi \right)$$