Metamath Proof Explorer


Theorem opelxp2

Description: The second member of an ordered pair of classes in a Cartesian product belongs to second Cartesian product argument. (Contributed by Mario Carneiro, 26-Apr-2015)

Ref Expression
Assertion opelxp2 ( ⟨ 𝐴 , 𝐵 ⟩ ∈ ( 𝐶 × 𝐷 ) → 𝐵𝐷 )

Proof

Step Hyp Ref Expression
1 opelxp ( ⟨ 𝐴 , 𝐵 ⟩ ∈ ( 𝐶 × 𝐷 ) ↔ ( 𝐴𝐶𝐵𝐷 ) )
2 1 simprbi ( ⟨ 𝐴 , 𝐵 ⟩ ∈ ( 𝐶 × 𝐷 ) → 𝐵𝐷 )