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Theorem ordtcon 26495
Description: Connectedness in the order topology of a complete uniform totally ordered space. (Contributed by Thierry Arnoux, 15-Sep-2018.)
Hypotheses
Ref Expression
ordtcon.x  |-  B  =  ( Base `  K
)
ordtcon.l  |-  .<_  =  ( ( le `  K
)  i^i  ( B  X.  B ) )
ordtcon.j  |-  J  =  (ordTop `  .<_  )
Assertion
Ref Expression
ordtcon  |- T.

Proof of Theorem ordtcon
StepHypRef Expression
1 tru 1374 1  |- T.
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   T. wtru 1371    i^i cin 3430    X. cxp 4941   ` cfv 5521   Basecbs 14287   lecple 14359  ordTopcordt 14551
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-tru 1373
This theorem is referenced by: (None)
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