Theorem fvconst2g

Description: The value of a constant function. (Contributed by NM, 20-Aug-2005)

	Ref	Expression
Assertion	fvconst2g	$$⊢\left(B\in D\wedge C\in A\right)\to \left(A\times \left\{B\right\}\right)\left(C\right)=B$$

Proof

Step	Hyp	Ref	Expression
1		fconstg	$$⊢B\in D\to \left(A\times \left\{B\right\}\right):A⟶\left\{B\right\}$$
2		fvconst	$$⊢\left(\left(A\times \left\{B\right\}\right):A⟶\left\{B\right\}\wedge C\in A\right)\to \left(A\times \left\{B\right\}\right)\left(C\right)=B$$
3	1 2	sylan	$$⊢\left(B\in D\wedge C\in A\right)\to \left(A\times \left\{B\right\}\right)\left(C\right)=B$$