Metamath Proof Explorer


Theorem fconst6

Description: A constant function as a mapping. (Contributed by Jeff Madsen, 30-Nov-2009) (Revised by Mario Carneiro, 22-Apr-2015)

Ref Expression
Hypothesis fconst6.1 ⊢ 𝐵 ∈ 𝐶
Assertion fconst6 ( 𝐴 × { 𝐵 } ) : 𝐴 ⟶ 𝐶

Proof

Step Hyp Ref Expression
1 fconst6.1 ⊢ 𝐵 ∈ 𝐶
2 fconst6g ⊢ ( 𝐵 ∈ 𝐶 → ( 𝐴 × { 𝐵 } ) : 𝐴 ⟶ 𝐶 )
3 1 2 ax-mp ⊢ ( 𝐴 × { 𝐵 } ) : 𝐴 ⟶ 𝐶