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Theorem cnvsom 5126
 Description: The converse of a strict order relation is a strict order relation. (Contributed by Jim Kingdon, 19-Dec-2018.)
Assertion
Ref Expression
cnvsom
Distinct variable groups:   ,   ,

Proof of Theorem cnvsom
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cnvpom 5125 . . 3
2 vex 2715 . . . . . . . . 9
3 vex 2715 . . . . . . . . 9
42, 3brcnv 4766 . . . . . . . 8
5 vex 2715 . . . . . . . . . . 11
62, 5brcnv 4766 . . . . . . . . . 10
75, 3brcnv 4766 . . . . . . . . . 10
86, 7orbi12i 754 . . . . . . . . 9
9 orcom 718 . . . . . . . . 9
108, 9bitri 183 . . . . . . . 8
114, 10imbi12i 238 . . . . . . 7
1211ralbii 2463 . . . . . 6
13122ralbii 2465 . . . . 5
14 ralcom 2620 . . . . 5
1513, 14bitr3i 185 . . . 4
1615a1i 9 . . 3
171, 16anbi12d 465 . 2
18 df-iso 4256 . 2
19 df-iso 4256 . 2
2017, 18, 193bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wo 698  wex 1472   wcel 2128  wral 2435   class class class wbr 3965   wpo 4253   wor 4254  ccnv 4582 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4134  ax-pr 4168 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pw 3545  df-sn 3566  df-pr 3567  df-op 3569  df-br 3966  df-opab 4026  df-po 4255  df-iso 4256  df-cnv 4591 This theorem is referenced by:  gtso  7939
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