Theorem bdayfn

Description: The birthday function is a function over No . (Contributed by Scott Fenton, 30-Jun-2011)

	Ref	Expression
Assertion	bdayfn	$$⊢\mathrm{bday}Fn\mathrm{No}$$

Proof

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