Theorem lerel 11304

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 11303	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5677	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5765	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3931   × cxp 5657  Rel wrel 5664  ℝ^*cxr 11273   ≤ cle 11275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466  df-dif 3934  df-ss 3948  df-opab 5187  df-xp 5665  df-rel 5666  df-le 11280

This theorem is referenced by:  dfle2  13168  dflt2  13169  ledm  18605  lern  18606  lefld  18607  letsr  18608  dvle  25969  gtiso  32683