Theorem lerel 11323

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 11322	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5707	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5794	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3963   × cxp 5687  Rel wrel 5694  ℝ^*cxr 11292   ≤ cle 11294

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-ss 3980  df-opab 5211  df-xp 5695  df-rel 5696  df-le 11299

This theorem is referenced by:  dfle2  13186  dflt2  13187  ledm  18648  lern  18649  lefld  18650  letsr  18651  dvle  26061  gtiso  32716