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Metamath Proof Explorer

Theorem s3eq2

Description: Equality theorem for a length 3 word for the second symbol. (Contributed by AV, 4-Jan-2022)

		Ref	Expression
	Assertion	s3eq2	$⊢ B = D \to ⟨“ A B C ”⟩ = ⟨“ A D C ”⟩$

Step	Hyp	Ref	Expression
1		eqidd	$⊢ B = D \to A = A$
2		id	$⊢ B = D \to B = D$
3		eqidd	$⊢ B = D \to C = C$
4	1 2 3	s3eqd	$⊢ B = D \to ⟨“ A B C ”⟩ = ⟨“ A D C ”⟩$