Theorem bdaydm

Description: The birthday function's domain is No . (Contributed by Scott Fenton, 14-Jun-2011)

	Ref	Expression
Assertion	bdaydm	$$⊢\mathrm{dom}\mathrm{bday}=\mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		bdayfo	$$⊢\mathrm{bday}:\mathrm{No}\underset{onto}{⟶}\mathrm{On}$$
2		fof	$$⊢\mathrm{bday}:\mathrm{No}\underset{onto}{⟶}\mathrm{On}\to \mathrm{bday}:\mathrm{No}⟶\mathrm{On}$$
3	1 2	ax-mp	$$⊢\mathrm{bday}:\mathrm{No}⟶\mathrm{On}$$
4	3	fdmi	$$⊢\mathrm{dom}\mathrm{bday}=\mathrm{No}$$