Theorem dfsb7ALT

Description: Alternate version of dfsb7 . (Contributed by NM, 28-Jan-2004) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfsb1.p9	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
Assertion	dfsb7ALT	$$⊢\theta \leftrightarrow \exists z\left(z=y\wedge \exists x\left(x=z\wedge \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		dfsb1.p9	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
2		nfv	$$⊢Ⅎz\phi$$
3	1 2	sb7fALT	$$⊢\theta \leftrightarrow \exists z\left(z=y\wedge \exists x\left(x=z\wedge \phi \right)\right)$$