Metamath Proof Explorer


Theorem 0ov

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

Ref Expression
Assertion 0ov ( 𝐴𝐵 ) = ∅

Proof

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