Theorem 2fveq3

Description: Equality theorem for nested function values. (Contributed by AV, 14-Aug-2022)

	Ref	Expression
Assertion	2fveq3	⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ ( 𝐺 ‘ 𝐴 ) ) = ( 𝐹 ‘ ( 𝐺 ‘ 𝐵 ) ) )

Proof

Step	Hyp	Ref	Expression
1		fveq2	⊢ ( 𝐴 = 𝐵 → ( 𝐺 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 ) )
2	1	fveq2d	⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ ( 𝐺 ‘ 𝐴 ) ) = ( 𝐹 ‘ ( 𝐺 ‘ 𝐵 ) ) )