Theorem lerel 11200

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 11199	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5642	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5731	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3890   × cxp 5622  Rel wrel 5629  ℝ^*cxr 11169   ≤ cle 11171

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-dif 3893  df-ss 3907  df-opab 5149  df-xp 5630  df-rel 5631  df-le 11176

This theorem is referenced by:  dfle2  13089  dflt2  13090  ledm  18547  lern  18548  lefld  18549  letsr  18550  dvle  25984  gtiso  32789