Metamath Proof Explorer


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