Theorem equsb1ALT

Description: Alternate version of equsb1 . (Contributed by NM, 10-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfsb1.p4	$$⊢\theta \leftrightarrow \left(\left(x=y\to x=y\right)\wedge \exists x\left(x=y\wedge x=y\right)\right)$$
Assertion	equsb1ALT	$$⊢\theta$$

Proof

Step	Hyp	Ref	Expression
1		dfsb1.p4	$$⊢\theta \leftrightarrow \left(\left(x=y\to x=y\right)\wedge \exists x\left(x=y\wedge x=y\right)\right)$$
2	1	sb2ALT	$$⊢\forall x\left(x=y\to x=y\right)\to \theta$$
3		id	$$⊢x=y\to x=y$$
4	2 3	mpg	$$⊢\theta$$