Theorem lerel 11354

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 11353	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5718	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5805	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3976   × cxp 5698  Rel wrel 5705  ℝ^*cxr 11323   ≤ cle 11325

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-dif 3979  df-ss 3993  df-opab 5229  df-xp 5706  df-rel 5707  df-le 11330

This theorem is referenced by:  dfle2  13209  dflt2  13210  ledm  18660  lern  18661  lefld  18662  letsr  18663  dvle  26066  gtiso  32712