Theorem nfab1 2351

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 2196	. 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}
2	1	nfci 2339	1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Syntax hints:  {cab 2192  Ⅎwnfc 2336

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2193  df-nfc 2338

This theorem is referenced by:  abid2f  2375  nfrab1  2687  elabgt  2916  elabgf  2917  nfsbc1d  3017  ss2ab  3263  abn0r  3487  euabsn  3705  iunab  3977  iinab  3992  iotaexab  5256  sniota  5268  nfixp1  6815  elabgft1  15828  elabgf2  15830