Theorem nfab1 2221

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 2071	. 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}
2	1	nfci 2209	1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Syntax hints:  {cab 2067  Ⅎwnfc 2206

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-nfc 2208

This theorem is referenced by:  abid2f  2243  nfrab1  2533  elabgt  2735  elabgf  2736  nfsbc1d  2831  ss2ab  3062  abn0r  3270  euabsn  3462  iunab  3724  iinab  3739  sniota  4914  elabgft1  10588  elabgf2  10590