Theorem lerel 11326

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 11325	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5702	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5790	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3950   × cxp 5682  Rel wrel 5689  ℝ^*cxr 11295   ≤ cle 11297

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-ss 3967  df-opab 5205  df-xp 5690  df-rel 5691  df-le 11302

This theorem is referenced by:  dfle2  13190  dflt2  13191  ledm  18636  lern  18637  lefld  18638  letsr  18639  dvle  26047  gtiso  32711