Some mathematicians do have a definite over-fondness for handwaving away statements they can't be bothered to prove with the "it follows trivially that ...". It's all well and good when such a proof would be 20 minutes of basic algebra, but that's frequently not the case.

One of our lecturers at university was so renowned for this, everyone taking that module organised to write "the answer to this question is trivial, and is left as an exercise to the marker" for any question they couldn't figure out in the exam.