Theorem eliminable1 37522

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 2741	1 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} ↔ [𝑦 / 𝑥]𝜑)

This proof depends on syntax axioms:   ↔ wb 209  [wsb 2095   ∈ wcel 2142  {cab 2740

This proof depends on definitions:  df-clab 2741

This theorem is used by: (None)