Theorem nfaba1g 2906

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2365. See nfaba1 2905 for a version with a disjoint variable condition, but not requiring ax-13 2365. (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 2140	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfabg 2904	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1531  {cab 2703  Ⅎwnfc 2877

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-11 2146  ax-12 2163  ax-13 2365

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704  df-nfc 2879

This theorem is referenced by: (None)