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Theorem nfab1 2257
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfab1 𝑥{𝑥𝜑}

Proof of Theorem nfab1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 nfsab1 2105 . 2 𝑥 𝑦 ∈ {𝑥𝜑}
21nfci 2245 1 𝑥{𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2101  wnfc 2242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-nfc 2244
This theorem is referenced by:  abid2f  2280  nfrab1  2584  elabgt  2795  elabgf  2796  nfsbc1d  2894  ss2ab  3131  abn0r  3353  euabsn  3559  iunab  3825  iinab  3840  sniota  5073  nfixp1  6566  elabgft1  12677  elabgf2  12679
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