Theorem bdayrn

Description: The birthday function's range is On . (Contributed by Scott Fenton, 14-Jun-2011)

	Ref	Expression
Assertion	bdayrn	⊢ ran bday = On

Proof

Step	Hyp	Ref	Expression
1		bdayfo	⊢ bday : No ⟶onto On
2		forn	⊢ ( bday : No ⟶onto On → ran bday = On )
3	1 2	ax-mp	⊢ ran bday = On