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Metamath Proof Explorer

Theorem cardeqv

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

		Ref	Expression
	Assertion	cardeqv	$⊢ dom card = V$

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