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Theorem lerel 11215
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 11214 . 2 ≤ ⊆ (ℝ* × ℝ*)
2 relxp 5649 . 2 Rel (ℝ* × ℝ*)
3 relss 5735 . 2 ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
41, 2, 3mp2 9 1 Rel ≤
Colors of variables: wff setvar class
Syntax hints:  wss 3908   × cxp 5629  Rel wrel 5636  *cxr 11184  cle 11186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3445  df-dif 3911  df-in 3915  df-ss 3925  df-opab 5166  df-xp 5637  df-rel 5638  df-le 11191
This theorem is referenced by:  dfle2  13058  dflt2  13059  ledm  18471  lern  18472  lefld  18473  letsr  18474  dvle  25355  gtiso  31498
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