Theorem nfaba1g 2902

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2366. See nfaba1 2900 for a version with a disjoint variable condition, but not requiring ax-13 2366. (Contributed by Mario Carneiro, 14-Oct-2016.) (New usage is discouraged.)

Assertion

Ref	Expression
nfaba1g	⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Proof of Theorem nfaba1g

Step	Hyp	Ref	Expression
1		nfa1 2141	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfabg 2899	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1532  {cab 2703  Ⅎwnfc 2876

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-11 2147  ax-12 2167  ax-13 2366

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2704  df-nfc 2878

This theorem is referenced by: (None)