Theorem eliminable-velab 34569

Description: A theorem used to prove the base case of the Eliminability Theorem (see section comment): variable belongs to abstraction. (Contributed by BJ, 30-Apr-2024.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem eliminable-velab

Step	Hyp	Ref	Expression
1		df-clab 2737	1 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑)

Syntax hints:   ↔ wb 209  [wsb 2070   ∈ wcel 2112  {cab 2736

This theorem depends on definitions:  df-clab 2737

This theorem is referenced by:  eliminable-veqab  34570  eliminable-abeqv  34571  eliminable-abeqab  34572  eliminable-abelab  34574