Theorem ordtconn 29971

Description: Connectedness in the order topology of a complete uniform totally ordered space. (Contributed by Thierry Arnoux, 15-Sep-2018.)

Hypotheses

Ref	Expression
ordtconn.x	|- B = ( Base ` K )
ordtconn.l	|- .<_ = ( ( le ` K ) i^i ( B X. B ) )
ordtconn.j	|- J = (ordTop ` .<_ )

Assertion

Ref	Expression
ordtconn	|- T.

Proof of Theorem ordtconn

Step	Hyp	Ref	Expression
1		tru 1487	1 |- T.

Syntax hints:   = wceq 1483   T. wtru 1484   i^i cin 3573   X. cxp 5112   ` cfv 5888   Basecbs 15857   lecple 15948  ordTopcordt 16159

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 197  df-tru 1486

This theorem is referenced by: (None)