on condition that

Related to on condition that: conditional probability

on condition (that)

Only with the restriction that (something be the case). The company agreed to the sale, on condition that all their staff be absorbed by the larger company, with no forced layoffs. We won't kick you out of the house on condition you get treatment for your addiction. He was released from prison on condition of house arrest.
See also: condition, on
Farlex Dictionary of Idioms.

on condition that

Provided that, with the restriction that, as in She said she'd help with the costumes on condition that she would get ten free tickets to the play . The use of the noun condition in the sense of "stipulation" dates from the late 1300s, and the precise phrase from the early 1500s.
See also: condition, on, that
The American Heritage® Dictionary of Idioms by Christine Ammer.
See also:
  • on condition (that)
  • a hatchet man
  • hatchet man
  • go public
  • turkey bacon
  • tiger in (one's) tank
  • a tiger in your tank
  • company
  • put in touch with
  • put somebody in touch with somebody/something