Theorem lerel

Description: "Less than or equal to" is a relation. (Contributed by FL, 2-Aug-2009) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	lerel	$$⊢\mathrm{Rel}\le$$

Proof

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