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 ) e. On

Proof

Step	Hyp	Ref	Expression
1		cardf2	|- card : { x | E. y e. On y ~~ x } --> On
2		0elon	|- (/) e. On
3	1 2	f0cli	|- ( card ` A ) e. On