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Theorem oplecon3b 29683
 Description: Contraposition law for orthoposets. (chsscon3 22955 analog.) (Contributed by NM, 4-Nov-2011.)
Hypotheses
Ref Expression
opcon3.b
opcon3.l
opcon3.o
Assertion
Ref Expression
oplecon3b

Proof of Theorem oplecon3b
StepHypRef Expression
1 opcon3.b . . 3
2 opcon3.l . . 3
3 opcon3.o . . 3
41, 2, 3oplecon3 29682 . 2
5 simp1 957 . . . 4
61, 3opoccl 29677 . . . . 5
763adant2 976 . . . 4
81, 3opoccl 29677 . . . . 5
983adant3 977 . . . 4
101, 2, 3oplecon3 29682 . . . 4
115, 7, 9, 10syl3anc 1184 . . 3
121, 3opococ 29678 . . . . 5
13123adant3 977 . . . 4
141, 3opococ 29678 . . . . 5
15143adant2 976 . . . 4
1613, 15breq12d 4185 . . 3
1711, 16sylibd 206 . 2
184, 17impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1649   wcel 1721   class class class wbr 4172  cfv 5413  cbs 13424  cple 13491  coc 13492  cops 29655 This theorem is referenced by:  oplecon1b  29684  opltcon3b  29687  oldmm1  29700  omllaw4  29729  cvrcmp2  29767  glbconN  29859  lhpmod2i2  30520  lhpmod6i1  30521  lhprelat3N  30522  dochss  31848 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-nul 4298 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-sbc 3122  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-iota 5377  df-fv 5421  df-ov 6043  df-oposet 29659
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