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Theorem ltrel 11222
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 11221 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5652 . 2 Rel (ℝ* × ℝ*)
3 relss 5738 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
Colors of variables: wff setvar class
Syntax hints:  wss 3911   × cxp 5632  Rel wrel 5639  *cxr 11193   < clt 11194
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-un 3916  df-in 3918  df-ss 3928  df-pr 4590  df-opab 5169  df-xp 5640  df-rel 5641  df-xr 11198  df-ltxr 11199
This theorem is referenced by:  dflt2  13073  gtiso  31661
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