Theorem ltrel

Description: "Less than" is a relation. (Contributed by NM, 14-Oct-2005)

	Ref	Expression
Assertion	ltrel	⊢ Rel <

Proof

Step	Hyp	Ref	Expression
1		ltrelxr	⊢ < ⊆ ( ℝ* × ℝ* )
2		relxp	⊢ Rel ( ℝ* × ℝ* )
3		relss	⊢ ( < ⊆ ( ℝ* × ℝ* ) → ( Rel ( ℝ* × ℝ* ) → Rel < ) )
4	1 2 3	mp2	⊢ Rel <