Theorem seqeq1d

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

	Ref	Expression
Hypothesis	seqeqd.1	$$⊢\phi \to A=B$$
Assertion	seqeq1d	$$⊢\phi \to seqA\left(\underset{\dot{}}{+},F\right)=seqB\left(\underset{\dot{}}{+},F\right)$$

Proof

Step	Hyp	Ref	Expression
1		seqeqd.1	$$⊢\phi \to A=B$$
2		seqeq1	$$⊢A=B\to seqA\left(\underset{\dot{}}{+},F\right)=seqB\left(\underset{\dot{}}{+},F\right)$$
3	1 2	syl	$$⊢\phi \to seqA\left(\underset{\dot{}}{+},F\right)=seqB\left(\underset{\dot{}}{+},F\right)$$