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Metamath Proof Explorer

Theorem oteq3d

Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017)

		Ref	Expression
	Hypothesis	oteq1d.1	$⊢ φ \to A = B$
	Assertion	oteq3d	$⊢ φ \to ⟨C, D, A⟩ = ⟨C, D, B⟩$

Step	Hyp	Ref	Expression
1		oteq1d.1	$⊢ φ \to A = B$
2		oteq3	$⊢ A = B \to ⟨C, D, A⟩ = ⟨C, D, B⟩$
3	1 2	syl	$⊢ φ \to ⟨C, D, A⟩ = ⟨C, D, B⟩$