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Metamath Proof Explorer

Theorem sdomnen

Description: Strict dominance implies non-equinumerosity. (Contributed by NM, 10-Jun-1998)

		Ref	Expression
	Assertion	sdomnen	$⊢ A ≺ B \to \neg A \approx B$

Step	Hyp	Ref	Expression
1		brsdom	$⊢ A ≺ B \leftrightarrow (A ≼ B \land \neg A \approx B)$
2	1	simprbi	$⊢ A ≺ B \to \neg A \approx B$