Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eliminable1 Structured version   Visualization version   GIF version

Theorem eliminable1 31864
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.)
Assertion
Ref Expression
eliminable1 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)

Proof of Theorem eliminable1
StepHypRef Expression
1 df-clab 2501 1 (𝑦 ∈ {𝑥𝜑} ↔ [𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 194  [wsb 1830  wcel 1938  {cab 2500
This theorem depends on definitions:  df-clab 2501
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator