Theorem ordtconn 34324

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 1573	1 ⊢ ⊤

This proof depends on syntax axioms:   = wceq 1569  ⊤wtru 1570   ∩ cin 3903   × cxp 5658  ‘cfv 6536  Basecbs 17275  lecple 17323  ordTopcordt 17559

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572

This theorem is used by: (None)