Theorem lerel 11196

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 11195	. 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 3901   × cxp 5622  Rel wrel 5629  ℝ^*cxr 11165   ≤ cle 11167

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-dif 3904  df-ss 3918  df-opab 5161  df-xp 5630  df-rel 5631  df-le 11172

This theorem is referenced by:  dfle2  13061  dflt2  13062  ledm  18513  lern  18514  lefld  18515  letsr  18516  dvle  25968  gtiso  32780