Theorem nfaba1g 2935

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2404. See nfaba1 2934 for a version with a disjoint variable condition, but not requiring ax-13 2404. (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 2191	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfabg 2933	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

This proof depends on syntax axioms:  ∀wal 1568  {cab 2741  Ⅎwnfc 2911

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-10 2180  ax-11 2197  ax-12 2216  ax-13 2404

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-sb 2102  df-clab 2742  df-nfc 2913

This theorem is used by: (None)