Theorem seqeq2d

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

	Ref	Expression
Hypothesis	seqeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	seqeq2d	⊢ ( 𝜑 → seq 𝑀 ( 𝐴 , 𝐹 ) = seq 𝑀 ( 𝐵 , 𝐹 ) )

Proof

Step	Hyp	Ref	Expression
1		seqeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		seqeq2	⊢ ( 𝐴 = 𝐵 → seq 𝑀 ( 𝐴 , 𝐹 ) = seq 𝑀 ( 𝐵 , 𝐹 ) )
3	1 2	syl	⊢ ( 𝜑 → seq 𝑀 ( 𝐴 , 𝐹 ) = seq 𝑀 ( 𝐵 , 𝐹 ) )