Theorem afveq1

Description: Equality theorem for function value, analogous to fveq1 . (Contributed by Alexander van der Vekens, 22-Jul-2017)

	Ref	Expression
Assertion	afveq1	⊢ ( 𝐹 = 𝐺 → ( 𝐹 ''' 𝐴 ) = ( 𝐺 ''' 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐹 = 𝐺 → 𝐹 = 𝐺 )
2		eqidd	⊢ ( 𝐹 = 𝐺 → 𝐴 = 𝐴 )
3	1 2	afveq12d	⊢ ( 𝐹 = 𝐺 → ( 𝐹 ''' 𝐴 ) = ( 𝐺 ''' 𝐴 ) )