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Theorem ltrel 10695
 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 10694 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5566 . 2 Rel (ℝ* × ℝ*)
3 relss 5649 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3934   × cxp 5546  Rel wrel 5553  ℝ*cxr 10666   < clt 10667 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2791 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-v 3495  df-un 3939  df-in 3941  df-ss 3950  df-pr 4562  df-opab 5120  df-xp 5554  df-rel 5555  df-xr 10671  df-ltxr 10672 This theorem is referenced by:  dflt2  12533  gtiso  30428
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