The Mishna teaches that one should not begin a wedding meal or conduct Din prior to Mincha, lest he come to perhaps miss the Tefillah. We learn elsewhere (Shabbos 10a) that conducting a Din is a Mitzvah, as certainly is attending a wedding. Why should one not begin the Mitzvah at hand, even if it may lead to forfeiting a later Mitzvah – since we know that one who is involved in a Mitzvah is exempt from doing another?
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Perhaps one can say that בדיעבד if one started if he is involved in a מצוה he need not stop, but לחתחילה one should not create such a situation.