Theorem nfab1 2321

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 2167	. 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}
2	1	nfci 2309	1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑}

Syntax hints:  {cab 2163  Ⅎwnfc 2306

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-nfc 2308

This theorem is referenced by:  abid2f  2345  nfrab1  2657  elabgt  2880  elabgf  2881  nfsbc1d  2981  ss2ab  3225  abn0r  3449  euabsn  3664  iunab  3935  iinab  3950  sniota  5209  nfixp1  6720  elabgft1  14615  elabgf2  14617