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Theorem ltrel 10301
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 10300 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 5266 . 2 Rel (ℝ* × ℝ*)
3 relss 5346 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 9 1 Rel <
Colors of variables: wff setvar class
Syntax hints:  wss 3721   × cxp 5247  Rel wrel 5254  *cxr 10274   < clt 10275
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-v 3351  df-un 3726  df-in 3728  df-ss 3735  df-pr 4317  df-opab 4845  df-xp 5255  df-rel 5256  df-xr 10279  df-ltxr 10280
This theorem is referenced by:  dflt2  12185  gtiso  29812
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