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Metamath Proof Explorer

Theorem sdomtr

Description: Strict dominance is transitive. Theorem 21(iii) of Suppes p. 97. (Contributed by NM, 9-Jun-1998)

		Ref	Expression
	Assertion	sdomtr	$⊢ (A ≺ B \land B ≺ C) \to A ≺ C$

Step	Hyp	Ref	Expression
1		sdomdom	$⊢ A ≺ B \to A ≼ B$
2		domsdomtr	$⊢ (A ≼ B \land B ≺ C) \to A ≺ C$
3	1 2	sylan	$⊢ (A ≺ B \land B ≺ C) \to A ≺ C$