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Theorem ltrel 7140
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 7139 . 2 < ⊆ (ℝ* × ℝ*)
2 relxp 4475 . 2 Rel (ℝ* × ℝ*)
3 relss 4455 . 2 ( < ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel < ))
41, 2, 3mp2 16 1 Rel <
Colors of variables: wff set class
Syntax hints:  wss 2945   × cxp 4371  Rel wrel 4378  *cxr 7118   < clt 7119
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-pr 3410  df-opab 3847  df-xp 4379  df-rel 4380  df-xr 7123  df-ltxr 7124
This theorem is referenced by: (None)
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