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	$$⊢\mathrm{card}\left(A\right)\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		cardf2	$$⊢\mathrm{card}:\left\{x|\exists y\in \mathrm{On}y\approx x\right\}⟶\mathrm{On}$$
2		0elon	$$⊢\varnothing \in \mathrm{On}$$
3	1 2	f0cli	$$⊢\mathrm{card}\left(A\right)\in \mathrm{On}$$