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Metamath Proof Explorer

Theorem ordwe

Description: Membership well-orders every ordinal. Proposition 7.4 of TakeutiZaring p. 36. (Contributed by NM, 3-Apr-1994)

		Ref	Expression
	Assertion	ordwe	$⊢ Ord A \to E We A$

Step	Hyp	Ref	Expression
1		df-ord	$⊢ Ord A \leftrightarrow (Tr A \land E We A)$
2	1	simprbi	$⊢ Ord A \to E We A$