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Metamath Proof Explorer

Theorem opeq12

Description: Equality theorem for ordered pairs. (Contributed by NM, 28-May-1995)

		Ref	Expression
	Assertion	opeq12	$⊢ (A = C \land B = D) \to ⟨A, B⟩ = ⟨C, D⟩$

Step	Hyp	Ref	Expression
1		opeq1	$⊢ A = C \to ⟨A, B⟩ = ⟨C, B⟩$
2		opeq2	$⊢ B = D \to ⟨C, B⟩ = ⟨C, D⟩$
3	1 2	sylan9eq	$⊢ (A = C \land B = D) \to ⟨A, B⟩ = ⟨C, D⟩$