Metamath Proof Explorer


Theorem oveq1d

Description: Equality deduction for operation value. (Contributed by NM, 13-Mar-1995)

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

Proof

Step Hyp Ref Expression
1 oveq1d.1 ⊢ ( 𝜑 → 𝐴 = 𝐵 )
2 oveq1 ⊢ ( 𝐴 = 𝐵 → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐶 ) )
3 1 2 syl ⊢ ( 𝜑 → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐶 ) )