Theorem lerel 11261

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

Assertion

Ref	Expression
lerel	⊢ Rel ≤

Proof of Theorem lerel

Step	Hyp	Ref	Expression
1		lerelxr 11260	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5669	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5758	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3907   × cxp 5649  Rel wrel 5656  ℝ^*cxr 11230   ≤ cle 11232

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-dif 3910  df-ss 3924  df-opab 5167  df-xp 5657  df-rel 5658  df-le 11237

This theorem is referenced by:  dfle2  13160  dflt2  13161  ledm  18634  lern  18635  lefld  18636  letsr  18637  dvle  26123  gtiso  32954