Theorem lerel 11274

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 11273	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5681	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5770	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3906   × cxp 5661  Rel wrel 5668  ℝ^*cxr 11243   ≤ cle 11245

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-dif 3909  df-ss 3923  df-opab 5175  df-xp 5669  df-rel 5670  df-le 11250

This theorem is referenced by:  dfle2  13173  dflt2  13174  ledm  18647  lern  18648  lefld  18649  letsr  18650  dvle  26147  gtiso  33027