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Metamath Proof Explorer

Theorem nfeu1ALT

Description: Alternate version of nfeu1 with a shorter proof but using ax-12 . Bound-variable hypothesis builder for uniqueness. See also nfeu1 . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	nfeu1ALT	$⊢ Ⅎ x \exists! x φ$

Proof

Step	Hyp	Ref	Expression
1		eu6	$⊢ \exists! x φ \leftrightarrow \exists y \forall x (φ \leftrightarrow x = y)$
2		nfexa2	$⊢ Ⅎ x \exists y \forall x (φ \leftrightarrow x = y)$
3	1 2	nfxfr	$⊢ Ⅎ x \exists! x φ$