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Metamath Proof Explorer

Theorem epn0

Description: The membership relation is nonempty. (Contributed by AV, 19-Jun-2022)

		Ref	Expression
	Assertion	epn0	⊢ E ≠ ∅

Step	Hyp	Ref	Expression
1		0sn0ep	⊢ ∅ E { ∅ }
2		brne0	⊢ ( ∅ E { ∅ } → E ≠ ∅ )
3	1 2	ax-mp	⊢ E ≠ ∅