Theorem opelxp1

Description: The first member of an ordered pair of classes in a Cartesian product belongs to first Cartesian product argument. (Contributed by NM, 28-May-2008) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	opelxp1	⊢ ( ⟨ 𝐴 , 𝐵 ⟩ ∈ ( 𝐶 × 𝐷 ) → 𝐴 ∈ 𝐶 )

Proof

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