Theorem nfab1 2388

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 2224	. 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}
2	1	nfci 2376	1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Syntax hints:  {cab 2220  Ⅎwnfc 2373

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-nfc 2375

This theorem is referenced by:  abid2f  2412  nfrab1  2726  elabgt  2960  elabgf  2961  nfsbc1d  3061  ss2ab  3308  abn0r  3535  euabsn  3763  iunab  4040  iinab  4055  iotaexab  5333  sniota  5345  nfixp1  6955  modom  7063  elabgft1  16599  elabgf2  16601