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Theorem ltrel 10052
Description: 'Less than' is a relation. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ltrel Rel <

Proof of Theorem ltrel
StepHypRef Expression
1 ltrelxr 10051 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5193 . 2 Rel (ℝ* × ℝ*)
3 relss 5172 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
Colors of variables: wff setvar class
Syntax hints:  wss 3559   × cxp 5077  Rel wrel 5084  *cxr 10025   < clt 10026
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3191  df-un 3564  df-in 3566  df-ss 3573  df-pr 4156  df-opab 4679  df-xp 5085  df-rel 5086  df-xr 10030  df-ltxr 10031
This theorem is referenced by:  dflt2  11933  gtiso  29344
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