Theorem cardeqv

Description: All sets are well-orderable under choice. (Contributed by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	cardeqv	$$⊢\mathrm{dom}\mathrm{card}=\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		axac3	$$⊢\mathrm{CHOICE}$$
2		dfac10	$$⊢\mathrm{CHOICE}\leftrightarrow \mathrm{dom}\mathrm{card}=\mathrm{V}$$
3	1 2	mpbi	$$⊢\mathrm{dom}\mathrm{card}=\mathrm{V}$$