Theorem fvoveq1d

Description: Equality deduction for nested function and operation value. (Contributed by AV, 23-Jul-2022)

	Ref	Expression
Hypothesis	fvoveq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	fvoveq1d	⊢ ( 𝜑 → ( 𝐹 ‘ ( 𝐴 𝑂 𝐶 ) ) = ( 𝐹 ‘ ( 𝐵 𝑂 𝐶 ) ) )

Proof

Step	Hyp	Ref	Expression
1		fvoveq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2	1	oveq1d	⊢ ( 𝜑 → ( 𝐴 𝑂 𝐶 ) = ( 𝐵 𝑂 𝐶 ) )
3	2	fveq2d	⊢ ( 𝜑 → ( 𝐹 ‘ ( 𝐴 𝑂 𝐶 ) ) = ( 𝐹 ‘ ( 𝐵 𝑂 𝐶 ) ) )