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Theorem nfab1 2180
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 2030 . 2 𝑥 𝑦 ∈ {𝑥𝜑}
21nfci 2168 1 𝑥{𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2026  wnfc 2165
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-nfc 2167
This theorem is referenced by:  abid2f  2202  nfrab1  2489  elabgt  2684  elabgf  2685  nfsbc1d  2780  ss2ab  3008  abn0r  3243  euabsn  3440  iunab  3703  iinab  3718  sniota  4894  elabgft1  9917  elabgf2  9919
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