Theorem sbfALT

Description: Alternate version of sbf . (Contributed by NM, 14-May-1993) (Revised by Mario Carneiro, 4-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	dfsb1.ph	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
	sbfALT.1	$$⊢Ⅎx\phi$$
Assertion	sbfALT	$$⊢\theta \leftrightarrow \phi$$

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		sbfALT.1	$$⊢Ⅎx\phi$$
3	1	sbftALT	$$⊢Ⅎx\phi \to \left(\theta \leftrightarrow \phi \right)$$
4	2 3	ax-mp	$$⊢\theta \leftrightarrow \phi$$