Theorem abid

Description: Simplification of class abstraction notation when the free and bound variables are identical. (Contributed by NM, 26-May-1993)

	Ref	Expression
Assertion	abid	⊢ ( 𝑥 ∈ { 𝑥 ∣ 𝜑 } ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		df-clab	⊢ ( 𝑥 ∈ { 𝑥 ∣ 𝜑 } ↔ [ 𝑥 / 𝑥 ] 𝜑 )
2		sbid	⊢ ( [ 𝑥 / 𝑥 ] 𝜑 ↔ 𝜑 )
3	1 2	bitri	⊢ ( 𝑥 ∈ { 𝑥 ∣ 𝜑 } ↔ 𝜑 )