Theorem lerel 11239

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 11238	. 2 ⊢ ≤ ⊆ (ℝ* × ℝ*)
2		relxp 5661	. 2 ⊢ Rel (ℝ* × ℝ*)
3		relss 5750	. 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
4	1, 2, 3	mp2 9	1 ⊢ Rel ≤

Syntax hints:   ⊆ wss 3902   × cxp 5641  Rel wrel 5648  ℝ^*cxr 11208   ≤ cle 11210

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-dif 3905  df-ss 3919  df-opab 5160  df-xp 5649  df-rel 5650  df-le 11215

This theorem is referenced by:  dfle2  13142  dflt2  13143  ledm  18612  lern  18613  lefld  18614  letsr  18615  dvle  26056  gtiso  32863