Theorem nfaba1g 2923

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2393. See nfaba1 2922 for a version with a disjoint variable condition, but not requiring ax-13 2393. (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 2175	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfabg 2921	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1548  {cab 2730  Ⅎwnfc 2899

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-10 2165  ax-11 2181  ax-12 2202  ax-13 2393

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-tru 1553  df-ex 1790  df-nf 1794  df-sb 2081  df-clab 2731  df-nfc 2901

This theorem is referenced by: (None)