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 Gino Giotto, 20-Jan-2024)

	Ref	Expression
Hypothesis	nfab.1	⊢ Ⅎ 𝑥 𝜑
Assertion	nfab	⊢ Ⅎ 𝑥 { 𝑦 ∣ 𝜑 }

Proof

Step	Hyp	Ref	Expression
1		nfab.1	⊢ Ⅎ 𝑥 𝜑
2	1	nfsab	⊢ Ⅎ 𝑥 𝑧 ∈ { 𝑦 ∣ 𝜑 }
3	2	nfci	⊢ Ⅎ 𝑥 { 𝑦 ∣ 𝜑 }