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Metamath Proof Explorer

Theorem nfab

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016) Add disjoint variable condition to avoid ax-13 . See nfabg for a less restrictive version requiring more axioms. (Revised by GG, 20-Jan-2024)

		Ref	Expression
	Hypothesis	nfab.1	$⊢ Ⅎ x φ$
	Assertion	nfab	$⊢ \underline{Ⅎ} x \{y \| φ\}$

Proof

Step	Hyp	Ref	Expression
1		nfab.1	$⊢ Ⅎ x φ$
2	1	nfsab	$⊢ Ⅎ x z \in \{y \| φ\}$
3	2	nfci	$⊢ \underline{Ⅎ} x \{y \| φ\}$