Theorem bdayfun

Description: The birthday function is a function. (Contributed by Scott Fenton, 14-Jun-2011)

	Ref	Expression
Assertion	bdayfun	$$⊢\mathrm{Fun}\mathrm{bday}$$

Proof

Step	Hyp	Ref	Expression
1		bdayfo	$$⊢\mathrm{bday}:\mathrm{No}\underset{onto}{⟶}\mathrm{On}$$
2		fofun	$$⊢\mathrm{bday}:\mathrm{No}\underset{onto}{⟶}\mathrm{On}\to \mathrm{Fun}\mathrm{bday}$$
3	1 2	ax-mp	$$⊢\mathrm{Fun}\mathrm{bday}$$