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.)

Assertion

Ref	Expression
eliminable1	⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑)

Proof of Theorem eliminable1

Step	Hyp	Ref	Expression
1		df-clab 2597	1 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑)

Syntax hints:   ↔ wb 195  [wsb 1867   ∈ wcel 1977  {cab 2596

This theorem depends on definitions:  df-clab 2597

This theorem is referenced by: (None)