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Metamath Proof Explorer

Theorem ensdomtr

Description: Transitivity of equinumerosity and strict dominance. (Contributed by NM, 26-Oct-2003) (Revised by Mario Carneiro, 26-Apr-2015)

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

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