Theorem seqeq1d

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

	Ref	Expression
Hypothesis	seqeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	seqeq1d	⊢ ( 𝜑 → seq 𝐴 ( + , 𝐹 ) = seq 𝐵 ( + , 𝐹 ) )

Proof

Step	Hyp	Ref	Expression
1		seqeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		seqeq1	⊢ ( 𝐴 = 𝐵 → seq 𝐴 ( + , 𝐹 ) = seq 𝐵 ( + , 𝐹 ) )
3	1 2	syl	⊢ ( 𝜑 → seq 𝐴 ( + , 𝐹 ) = seq 𝐵 ( + , 𝐹 ) )