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Theorem cnvsom 4861
 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 4860 . . 3
2 vex 2560 . . . . . . . . 9
3 vex 2560 . . . . . . . . 9
42, 3brcnv 4518 . . . . . . . 8
5 vex 2560 . . . . . . . . . . 11
62, 5brcnv 4518 . . . . . . . . . 10
75, 3brcnv 4518 . . . . . . . . . 10
86, 7orbi12i 681 . . . . . . . . 9
9 orcom 647 . . . . . . . . 9
108, 9bitri 173 . . . . . . . 8
114, 10imbi12i 228 . . . . . . 7
1211ralbii 2330 . . . . . 6
13122ralbii 2332 . . . . 5
14 ralcom 2473 . . . . 5
1513, 14bitr3i 175 . . . 4
1615a1i 9 . . 3
171, 16anbi12d 442 . 2
18 df-iso 4034 . 2
19 df-iso 4034 . 2
2017, 18, 193bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wo 629  wex 1381   wcel 1393  wral 2306   class class class wbr 3764   wpo 4031   wor 4032  ccnv 4344 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-po 4033  df-iso 4034  df-cnv 4353 This theorem is referenced by:  gtso  7097
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