Metamath Proof Explorer

Theorem cardon

Description: The cardinal number of a set is an ordinal number. Proposition 10.6(1) of TakeutiZaring p. 85. (Contributed by Mario Carneiro, 7-Jan-2013) (Revised by Mario Carneiro, 13-Sep-2013)

Ref Expression
Assertion cardon card A On


Step Hyp Ref Expression
1 cardf2 card : x | y On y x On
2 0elon On
3 1 2 f0cli card A On