Theorem ltrel

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

	Ref	Expression
Assertion	ltrel	$$⊢\mathrm{Rel}<$$

Proof

Step	Hyp	Ref	Expression
1		ltrelxr	$$⊢<\subseteq {ℝ}^{*}\times {ℝ}^{*}$$
2		relxp	$$⊢\mathrm{Rel}\left({ℝ}^{*}\times {ℝ}^{*}\right)$$
3		relss	$$⊢<\subseteq {ℝ}^{*}\times {ℝ}^{*}\to \left(\mathrm{Rel}\left({ℝ}^{*}\times {ℝ}^{*}\right)\to \mathrm{Rel}<\right)$$
4	1 2 3	mp2	$$⊢\mathrm{Rel}<$$