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Theorem socnv 33074
 Description: The converse of a strict ordering is still a strict ordering. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
socnv (𝑅 Or 𝐴𝑅 Or 𝐴)

Proof of Theorem socnv
StepHypRef Expression
1 cnvso 6117 . 2 (𝑅 Or 𝐴𝑅 Or 𝐴)
21biimpi 219 1 (𝑅 Or 𝐴𝑅 Or 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   Or wor 5450  ◡ccnv 5531 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2622  df-eu 2653  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ne 3012  df-ral 3135  df-v 3471  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-if 4440  df-sn 4540  df-pr 4542  df-op 4546  df-br 5043  df-opab 5105  df-po 5451  df-so 5452  df-cnv 5540 This theorem is referenced by: (None)
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