Theorem seqeq3d

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	seqeq3d	$$⊢\phi \to seqM\left(\underset{\dot{}}{+},A\right)=seqM\left(\underset{\dot{}}{+},B\right)$$

Proof

Step	Hyp	Ref	Expression
1		seqeqd.1	$$⊢\phi \to A=B$$
2		seqeq3	$$⊢A=B\to seqM\left(\underset{\dot{}}{+},A\right)=seqM\left(\underset{\dot{}}{+},B\right)$$
3	1 2	syl	$$⊢\phi \to seqM\left(\underset{\dot{}}{+},A\right)=seqM\left(\underset{\dot{}}{+},B\right)$$