Rav Yehuda uses this phrase at the very end of the first column of page 29 of Tannait in the Babylonian Talmud:
אמר רב יהודה בריה דרב שמואל בר שילת משמיה דרב: כשם שמשנכנס אב ממעטין בשמחה - כך משנכנס אדר מרבין בשמחה
Now, my Aramaic is far weaker than my non-too-strong hodgepodge of Biblical and Modern Hebrew, but I think Rav Yehuda is essentially saying that the minimization of happiness upon entering the month of Av (when both the First and Second Temples were destroyed) is proportional to the maximization of happiness upon entering the month of Adar (the miracle of Purim and then soon after the miracles of the Exodus from Egypt into Eretz Yisrael).
Of course, משנכנס אדר מרבין בשמחה has inspired a song. I have not been able to figure out who wrote the upbeat, happy, and frankly awesome tune. However, here's a nice video of the Jerusalem Soul Center singing it last Rosh Chodesh Adar.
The Jerusalem Soul Center is, from what I've read, a center of hipster new age religious Zionism.