Theorem fvco3d

Description: Value of a function composition. Deduction form of fvco3 . (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	fvco3d.1	|- ( ph -> G : A --> B )
	fvco3d.2	|- ( ph -> C e. A )
Assertion	fvco3d	|- ( ph -> ( ( F o. G ) ` C ) = ( F ` ( G ` C ) ) )

Proof

Step	Hyp	Ref	Expression
1		fvco3d.1	|- ( ph -> G : A --> B )
2		fvco3d.2	|- ( ph -> C e. A )
3		fvco3	|- ( ( G : A --> B /\ C e. A ) -> ( ( F o. G ) ` C ) = ( F ` ( G ` C ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( ( F o. G ) ` C ) = ( F ` ( G ` C ) ) )