Theorem fvco3d

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

	Ref	Expression
Hypotheses	fvco3d.1	$$⊢\phi \to G:A⟶B$$
	fvco3d.2	$$⊢\phi \to C\in A$$
Assertion	fvco3d	$$⊢\phi \to \left(F\circ G\right)\left(C\right)=F\left(G\left(C\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		fvco3d.1	$$⊢\phi \to G:A⟶B$$
2		fvco3d.2	$$⊢\phi \to C\in A$$
3		fvco3	$$⊢\left(G:A⟶B\wedge C\in A\right)\to \left(F\circ G\right)\left(C\right)=F\left(G\left(C\right)\right)$$
4	1 2 3	syl2anc	$$⊢\phi \to \left(F\circ G\right)\left(C\right)=F\left(G\left(C\right)\right)$$