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Theorem nfab1 2225
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 2073 . 2 𝑥 𝑦 ∈ {𝑥𝜑}
21nfci 2213 1 𝑥{𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2069  wnfc 2210
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-nfc 2212
This theorem is referenced by:  abid2f  2247  nfrab1  2539  elabgt  2745  elabgf  2746  nfsbc1d  2842  ss2ab  3073  abn0r  3290  euabsn  3486  iunab  3750  iinab  3765  sniota  4961  elabgft1  11021  elabgf2  11023
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