Theorem ordtcon 29299

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) ∩ (𝐵 × 𝐵))
ordtcon.j	⊢ 𝐽 = (ordTop‘ ≤ )

Assertion

Ref	Expression
ordtcon	⊢ ⊤

Proof of Theorem ordtcon

Step	Hyp	Ref	Expression
1		tru 1479	1 ⊢ ⊤

Syntax hints:   = wceq 1475  ⊤wtru 1476   ∩ cin 3539   × cxp 5036  ‘cfv 5804  Basecbs 15695  lecple 15775  ordTopcordt 15982

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 196  df-tru 1478

This theorem is referenced by: (None)