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Theorem cnvti 6955
 Description: If a relation satisfies a condition corresponding to tightness of an apartness generated by an order, so does its converse. (Contributed by Jim Kingdon, 17-Dec-2021.)
Hypothesis
Ref Expression
eqinfti.ti
Assertion
Ref Expression
cnvti
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem cnvti
StepHypRef Expression
1 eqinfti.ti . . 3
2 ancom 264 . . 3
31, 2bitrdi 195 . 2
4 brcnvg 4764 . . . . 5
54notbid 657 . . . 4
6 brcnvg 4764 . . . . . 6
76ancoms 266 . . . . 5
87notbid 657 . . . 4
95, 8anbi12d 465 . . 3
109adantl 275 . 2
113, 10bitr4d 190 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   wcel 2128   class class class wbr 3965  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-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-cnv 4591 This theorem is referenced by:  eqinfti  6956  infvalti  6958  infclti  6959  inflbti  6960  infglbti  6961  infmoti  6964  infsnti  6966  infisoti  6968  infrenegsupex  9488  infxrnegsupex  11142
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