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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 ) → 𝐵 ∈ 𝐷 )

Proof

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