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Theorem nfab1 2196
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 2046 . 2 𝑥 𝑦 ∈ {𝑥𝜑}
21nfci 2184 1 𝑥{𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2042  wnfc 2181
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-nfc 2183
This theorem is referenced by:  abid2f  2218  nfrab1  2506  elabgt  2706  elabgf  2707  nfsbc1d  2802  ss2ab  3035  abn0r  3270  euabsn  3467  iunab  3730  iinab  3745  sniota  4921  elabgft1  10276  elabgf2  10278
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