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Theorem nfsab1 2179
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfsab1 𝑥 𝑦 ∈ {𝑥𝜑}
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfsab1
StepHypRef Expression
1 hbab1 2178 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nfi 1473 1 𝑥 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  wnf 1471  wcel 2160  {cab 2175
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176
This theorem is referenced by:  abbi  2303  nfab1  2334  ralab2  2916  rexab2  2918  abn0m  3463  rabn0m  3465  eluniab  3839  elintab  3873  intexabim  4173  iinexgm  4175  opabex3d  6150  opabex3  6151
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