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Theorem lerel 11224
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
StepHypRef Expression
1 lerelxr 11223 . 2 ≤ ⊆ (ℝ* × ℝ*)
2 relxp 5652 . 2 Rel (ℝ* × ℝ*)
3 relss 5738 . 2 ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
41, 2, 3mp2 9 1 Rel ≤
Colors of variables: wff setvar class
Syntax hints:  wss 3911   × cxp 5632  Rel wrel 5639  *cxr 11193  cle 11195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-in 3918  df-ss 3928  df-opab 5169  df-xp 5640  df-rel 5641  df-le 11200
This theorem is referenced by:  dfle2  13072  dflt2  13073  ledm  18484  lern  18485  lefld  18486  letsr  18487  dvle  25387  gtiso  31661
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