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Metamath Proof Explorer

Theorem numth3

Description: All sets are well-orderable under choice. (Contributed by Stefan O'Rear, 28-Feb-2015)

		Ref	Expression
	Assertion	numth3	$⊢ A \in V \to A \in dom card$

Step	Hyp	Ref	Expression
1		elex	$⊢ A \in V \to A \in V$
2		cardeqv	$⊢ dom card = V$
3	1 2	eleqtrrdi	$⊢ A \in V \to A \in dom card$