Theorem epn0

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

	Ref	Expression
Assertion	epn0	⊢ E ≠ ∅

Proof

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