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Theorem ltrel 9979
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 9978 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5150 . 2 Rel (ℝ* × ℝ*)
3 relss 5129 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
Colors of variables: wff setvar class
Syntax hints:  wss 3540   × cxp 5036  Rel wrel 5043  *cxr 9952   < clt 9953
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-pr 4128  df-opab 4644  df-xp 5044  df-rel 5045  df-xr 9957  df-ltxr 9958
This theorem is referenced by:  dflt2  11857  gtiso  28861
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