Theorem lerel 11238

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 11237	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5656	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5744	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3914   × cxp 5636  Rel wrel 5643  ℝ^*cxr 11207   ≤ cle 11209

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 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-dif 3917  df-ss 3931  df-opab 5170  df-xp 5644  df-rel 5645  df-le 11214

This theorem is referenced by:  dfle2  13107  dflt2  13108  ledm  18549  lern  18550  lefld  18551  letsr  18552  dvle  25912  gtiso  32624