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Theorem nfsab1 2599
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 2598 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nf5i 2010 1 𝑥 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wnf 1698  wcel 1976  {cab 2595
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2033  ax-13 2233
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596
This theorem is referenced by:  clelab  2734  nfab1  2752  ralab2  3337  rexab2  3339  eluniab  4377  elintab  4416  opabex3d  7014  opabex3  7015  setindtrs  36393  rababg  36681
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