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Metamath Proof Explorer

Theorem epel

Description: The membership relation and the membership predicate agree when the "containing" class is a setvar. Definition 1.6 of Schloeder p. 1. (Contributed by NM, 13-Aug-1995) Replace the first setvar variable with a class variable. (Revised by BJ, 13-Sep-2022)

		Ref	Expression
	Assertion	epel	⊢ ( 𝐴 E 𝑥 ↔ 𝐴 ∈ 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑥 ∈ V
2	1	epeli	⊢ ( 𝐴 E 𝑥 ↔ 𝐴 ∈ 𝑥 )