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Theorem ltrel 11324
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 11323 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5702 . 2 Rel (ℝ* × ℝ*)
3 relss 5790 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
Colors of variables: wff setvar class
Syntax hints:  wss 3950   × cxp 5682  Rel wrel 5689  *cxr 11295   < clt 11296
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-un 3955  df-ss 3967  df-pr 4628  df-opab 5205  df-xp 5690  df-rel 5691  df-xr 11300  df-ltxr 11301
This theorem is referenced by:  dflt2  13191  gtiso  32711
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