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Metamath Proof Explorer

Theorem 0ov

Description: Operation value of the empty set. (Contributed by AV, 15-May-2021)

		Ref	Expression
	Assertion	0ov	⊢ ( 𝐴 ∅ 𝐵 ) = ∅

Step	Hyp	Ref	Expression
1		df-ov	⊢ ( 𝐴 ∅ 𝐵 ) = ( ∅ ‘ ⟨ 𝐴 , 𝐵 ⟩ )
2		0fv	⊢ ( ∅ ‘ ⟨ 𝐴 , 𝐵 ⟩ ) = ∅
3	1 2	eqtri	⊢ ( 𝐴 ∅ 𝐵 ) = ∅