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Metamath Proof Explorer

Definition df-sdom

Description: Define the strict dominance relation. Alternate possible definitions are derived as brsdom and brsdom2 . Definition 3 of Suppes p. 97. (Contributed by NM, 31-Mar-1998)

		Ref	Expression
	Assertion	df-sdom	⊢ ≺ = ( ≼ ∖ ≈ )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		csdm	⊢ ≺
1		cdom	⊢ ≼
2		cen	⊢ ≈
3	1 2	cdif	⊢ ( ≼ ∖ ≈ )
4	0 3	wceq	⊢ ≺ = ( ≼ ∖ ≈ )