Theorem nfaba1g 2933

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2403. See nfaba1 2932 for a version with a disjoint variable condition, but not requiring ax-13 2403. (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 2185	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfabg 2931	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

This proof depends on syntax axioms:  ∀wal 1567  {cab 2740  Ⅎwnfc 2909

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-10 2175  ax-11 2191  ax-12 2212  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-ex 1809  df-nf 1813  df-sb 2096  df-clab 2741  df-nfc 2911

This theorem is used by: (None)