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Metamath Proof Explorer

Theorem seqeq1d

Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013)

		Ref	Expression
	Hypothesis	seqeqd.1	$⊢ φ \to A = B$
	Assertion	seqeq1d	$⊢ φ \to seq A (\underset{˙}{+}, F) = seq B (\underset{˙}{+}, F)$

Step	Hyp	Ref	Expression
1		seqeqd.1	$⊢ φ \to A = B$
2		seqeq1	$⊢ A = B \to seq A (\underset{˙}{+}, F) = seq B (\underset{˙}{+}, F)$
3	1 2	syl	$⊢ φ \to seq A (\underset{˙}{+}, F) = seq B (\underset{˙}{+}, F)$