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Theorem nfsab1 2600
 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 2599 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nf5i 2011 1 𝑥 𝑦 ∈ {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1699   ∈ wcel 1977  {cab 2596 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597 This theorem is referenced by:  clelab  2735  nfab1  2753  ralab2  3338  rexab2  3340  eluniab  4383  elintab  4422  opabex3d  7037  opabex3  7038  setindtrs  36610  rababg  36898
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