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Theorem eliminable1 32033
Description: A theorem used to prove the base case of the Eliminability Theorem (see section comment). (Contributed by BJ, 19-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Ref Expression
eliminable1 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)

Proof of Theorem eliminable1
StepHypRef Expression
1 df-clab 2597 1 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 195  [wsb 1867  wcel 1977  {cab 2596
This theorem depends on definitions:  df-clab 2597
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator