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Theorem nfsab1 2046
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 2045 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nfi 1367 1 𝑥 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  wnf 1365  wcel 1409  {cab 2042
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
This theorem is referenced by:  abbi  2167  nfab1  2196  ralab2  2728  rexab2  2730  rabn0m  3273  eluniab  3620  elintab  3654  intexabim  3934  iinexgm  3936  opabex3d  5776  opabex3  5777
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