Theorem spsbeOLDOLD

Description: Obsolete version of spsbe as of 7-Jul-2023. A specialization theorem. (Contributed by NM, 29-Jun-1993) (Proof shortened by Wolf Lammen, 3-May-2018) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	spsbeOLDOLD	$$⊢\left[y/x\right]\phi \to \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		sb1	$$⊢\left[y/x\right]\phi \to \exists x\left(x=y\wedge \phi \right)$$
2		exsimpr	$$⊢\exists x\left(x=y\wedge \phi \right)\to \exists x\phi$$
3	1 2	syl	$$⊢\left[y/x\right]\phi \to \exists x\phi$$