Theorem lerel 11284

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 11283	. 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 ≤

This proof depends on syntax axioms:   ⊆ wss 3906   × cxp 5661  Rel wrel 5668  ℝ^*cxr 11253   ≤ cle 11255

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-dif 3909  df-ss 3923  df-opab 5176  df-xp 5669  df-rel 5670  df-le 11260

This theorem is used by:  dfle2  13184  dflt2  13185  ledm  18664  lern  18665  lefld  18666  letsr  18667  dvle  26197  gtiso  33093