Theorem ordtconn 31172

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

Assertion

Ref	Expression
ordtconn	⊢ ⊤

Proof of Theorem ordtconn

Step	Hyp	Ref	Expression
1		tru 1540	1 ⊢ ⊤

Syntax hints:   = wceq 1536  ⊤wtru 1537   ∩ cin 3938   × cxp 5556  ‘cfv 6358  Basecbs 16486  lecple 16575  ordTopcordt 16775

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 209  df-tru 1539

This theorem is referenced by: (None)