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Theorem nfsab1OLD 2745
 Description: Obsolete version of nfsab1 2744 as of 20-Sep-2023. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfsab1OLD 𝑥 𝑦 ∈ {𝑥𝜑}
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfsab1OLD
StepHypRef Expression
1 hbab1 2743 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nf5i 2147 1 𝑥 𝑦 ∈ {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1785   ∈ wcel 2111  {cab 2735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2736 This theorem is referenced by: (None)
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