ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfsab1 GIF version

Theorem nfsab1 2079
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 2078 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nfi 1397 1 𝑥 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  wnf 1395  wcel 1439  {cab 2075
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076
This theorem is referenced by:  abbi  2202  nfab1  2231  ralab2  2780  rexab2  2782  abn0m  3312  rabn0m  3314  eluniab  3671  elintab  3705  intexabim  3994  iinexgm  3996  opabex3d  5906  opabex3  5907
  Copyright terms: Public domain W3C validator