"You can`t prove a negative."
"You cannot prove the non-existence of something."
"You cannot prove that something is impossible."
Often used as the alleged justification for the "What`s stated without proofs can be denied without proofs." one.
It is a *completely* made-up rule with no conceivable justification in any existing principle of logic, and in fact goes directly against the most basic and universally recognized laws of inference: as explained in "defaul denial", in logic (by the law of double negation) *any* statement can be thought as the negative of its complementary statement; therefore, to say "You can`t prove a negative" is the equivalent of saying: "Nothing can be proved", rendering all of logic completely meaningless.
It also goes against centuries of progress in both mathematics and natural sciences, both of which make extensive use of negative proofs in countless contexts: stuff like the non-existence of a 6th regular polihedron or of a stable chemical compound with formula S2H, the impossibility of squaring the cirle or achieving a perpetual-motion machine, are just some examples of a potentially endless list of negative statements that are both clearly provable and rigorously proven.
In logic, in absence of any proof either in favor or contrary to a claim, that claim has the same exact validity as its denial, and in no way the second position deserves a "privileged" treatment compared to the first one.
In order to give the slogan a semblance of validity, the pseudo-rationalist often ironically asks to prove the non-existence of blatantly imaginary stuff like "unicorns", "Santa-Claus" or "a teapot orbiting around the Sun", with the tacit implication that no one can do such a thing; aside from the intrinsic dishonesty of comparing a legit belief with actual basis (however weak they might be) with something that is deliberately made-up on the spot and no one believes into, proving the non-existence of such things is actually not only possible, but also extremely easy for anyone, by just drawing from universally accepted scientific knowledge or reasoning about elementary probability.