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Theorem lerel 7835
 Description: 'Less 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 7834 . 2 ≤ ⊆ (ℝ* × ℝ*)
2 relxp 4648 . 2 Rel (ℝ* × ℝ*)
3 relss 4626 . 2 ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ ))
41, 2, 3mp2 16 1 Rel ≤
 Colors of variables: wff set class Syntax hints:   ⊆ wss 3071   × cxp 4537  Rel wrel 4544  ℝ*cxr 7806   ≤ cle 7808 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-opab 3990  df-xp 4545  df-rel 4546  df-le 7813 This theorem is referenced by: (None)
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