Is it alright to put a 25mm tube in a 23mm tyre?

What you want to avoid is:

• a tube which, when deflated, or slightly inflated to a torus shape is already as wide as the inner space in the tire or wider. The tube should be quite a bit smaller than the inner tire chamber when slightly inflated.

• a tube with an excessive diameter: a situation when you slightly inflate the tube to insert it into the tire, and it is too large, so that it has to be awkwardly stuffed in there.

• a tube with too small a diameter which basically stretches onto the rim. It is possible, but installation is difficult.

  If a tube has a slightly small radius, but pre-inflating it expands the radius sufficiently that it can be comfortably stuffed into the tire, and the required inflation doesn't make the tube fatter than the tire chamber (the tire clinches onto the rim easily, and the tube doesn't get in the way), it is probably okay.

• a tube which is too thin relative to the tire, and has to stretch ridiculously. I use 700x(35-43)c in 45mm tires; I wouldn't want to go much narrower.

As far as the numbers on the box go, you can be slightly out of the tube's range. There is no such thing as a 23 mm tube. There are tubes which include 23 mm in their range. Your existing tubes in your 25 mm tires could already extend over the 23 mm range. Suppose your existing tubes are "22-25". Then, the 23 mm tires are in the middle of that range. Or suppose your tubes are 25-28. Then the 23 mm size is a bit out of range: it's okay to re-use the tubes if they pass the above avoid guidelines.