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Theorem opexmid 29942
 Description: Law of excluded middle for orthoposets. (chjo 23009 analog.) (Contributed by NM, 13-Sep-2011.)
Hypotheses
Ref Expression
opexmid.b
opexmid.o
opexmid.j
opexmid.u
Assertion
Ref Expression
opexmid

Proof of Theorem opexmid
StepHypRef Expression
1 opexmid.b . . . 4
2 eqid 2435 . . . 4
3 opexmid.o . . . 4
4 opexmid.j . . . 4
5 eqid 2435 . . . 4
6 eqid 2435 . . . 4
7 opexmid.u . . . 4
81, 2, 3, 4, 5, 6, 7oposlem 29918 . . 3
983anidm23 1243 . 2
109simp2d 970 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725   class class class wbr 4204  cfv 5446  (class class class)co 6073  cbs 13461  cple 13528  coc 13529  cjn 14393  cmee 14394  cp0 14458  cp1 14459  cops 29907 This theorem is referenced by:  dih1  32021 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-oposet 29911
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