Theorem relsdom

Description: Strict dominance is a relation. (Contributed by NM, 31-Mar-1998)

	Ref	Expression
Assertion	relsdom	⊢ Rel ≺

Proof

Step	Hyp	Ref	Expression
1		reldom	⊢ Rel ≼
2		reldif	⊢ ( Rel ≼ → Rel ( ≼ ∖ ≈ ) )
3		df-sdom	⊢ ≺ = ( ≼ ∖ ≈ )
4	3	releqi	⊢ ( Rel ≺ ↔ Rel ( ≼ ∖ ≈ ) )
5	2 4	sylibr	⊢ ( Rel ≼ → Rel ≺ )
6	1 5	ax-mp	⊢ Rel ≺