Theorem stdpc4ALT

Description: Alternate version of stdpc4 . (Contributed by NM, 14-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfsb1.ph	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
Assertion	stdpc4ALT	$$⊢\forall x\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		dfsb1.ph	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
2		ala1	$$⊢\forall x\phi \to \forall x\left(x=y\to \phi \right)$$
3	1	sb2ALT	$$⊢\forall x\left(x=y\to \phi \right)\to \theta$$
4	2 3	syl	$$⊢\forall x\phi \to \theta$$