Theorem nfab1 2314

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfab1	⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Proof of Theorem nfab1

Dummy variable 𝑦 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfsab1 2160	. 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}
2	1	nfci 2302	1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Syntax hints:  {cab 2156  Ⅎwnfc 2299

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-nfc 2301

This theorem is referenced by:  abid2f  2338  nfrab1  2649  elabgt  2871  elabgf  2872  nfsbc1d  2971  ss2ab  3215  abn0r  3439  euabsn  3653  iunab  3919  iinab  3934  sniota  5189  nfixp1  6696  elabgft1  13813  elabgf2  13815