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Theorem sopc 5934
 Description: Linear ordering as partial, connected relationship. (Contributed by SF, 12-Mar-2015.)
Assertion
Ref Expression
sopc (R Or A ↔ (R Po A R Connex A))

Proof of Theorem sopc
StepHypRef Expression
1 df-strict 5904 . . 3 Or = ( PoConnex )
21breqi 4645 . 2 (R Or AR( PoConnex )A)
3 brin 4693 . 2 (R( PoConnex )A ↔ (R Po A R Connex A))
42, 3bitri 240 1 (R Or A ↔ (R Po A R Connex A))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   ∩ cin 3208   class class class wbr 4639   Po cpartial 5891   Connex cconnex 5892   Or cstrict 5893 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-br 4640  df-strict 5904 This theorem is referenced by:  sod  5937  weds  5938  so0  5941  nchoicelem8  6296  nchoicelem19  6307
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