Theorem oveqd

Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006)

	Ref	Expression
Hypothesis	oveq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	oveqd	⊢ ( 𝜑 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) )

Proof

Step	Hyp	Ref	Expression
1		oveq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		oveq	⊢ ( 𝐴 = 𝐵 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) )