Theorem sb5OLD

Description: Obsolete version of sb5 as of 4-Sep-2023.) (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		sb6	$$⊢\left[y/x\right]\phi \leftrightarrow \forall x\left(x=y\to \phi \right)$$
2		sb56	$$⊢\exists x\left(x=y\wedge \phi \right)\leftrightarrow \forall x\left(x=y\to \phi \right)$$
3	1 2	bitr4i	$$⊢\left[y/x\right]\phi \leftrightarrow \exists x\left(x=y\wedge \phi \right)$$