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Theorem nfab1 2260
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 2107 . 2 𝑥 𝑦 ∈ {𝑥𝜑}
21nfci 2248 1 𝑥{𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2103  wnfc 2245
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-nfc 2247
This theorem is referenced by:  abid2f  2283  nfrab1  2587  elabgt  2799  elabgf  2800  nfsbc1d  2898  ss2ab  3135  abn0r  3357  euabsn  3563  iunab  3829  iinab  3844  sniota  5085  nfixp1  6580  elabgft1  12912  elabgf2  12914
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