Nothing proves it. The closest are Dunya's accusations, including her knowledge that he both discussed poison with her, AND went to get that poison.
"...Не твой револьвер, а Марфы Петровны, которую ты убил, злодей! У тебя ничего не было своего в ее доме. Я взяла его, как стала подозревать, на что ты способен."
"Ты жену отравил, я знаю, ты сам убийца!… Ты мне сам намекал; ты мне говорил об яде… я знаю, ты за ним ездил… у тебя было готово… Это непременно ты…"
"...этот ужасный человек, кажется, и был причиной ее смерти. Говорят, он ее ужасно избил!.."
"Я уверена, что он был причиною смерти покойницы Марфы Петровны..."
English (translated by Constance Garnett):
"It's not your revolver, it belonged to Marfa Petrovna, whom you killed, wretch! There was nothing of yours
in her house. I took it when I began to suspect what you were capable of."
"You poisoned your wife, I know; you are a murderer yourself!... You hinted it yourself; you talked to me of poison.... I know you went to get it... you had it in
readiness.... It was your doing...."
". . . that awful man seems to have been the
cause of her death. They say he beat her dreadfully."
"I am convinced that he was the cause of
Marfa Petrovna's death."
As well as his own admission he would have easily killed his wife if Dunya told him to:
Верите ли, я до того тогда врезался, что скажи она мне: зарежь или отрави Марфу Петровну и женись на мне, — это тотчас же было бы сделано!
Do you know, I was so wild about her at that time that if she had
told me to poison Marfa Petrovna or to cut her throat and to marry herself, it would have been done at once!
However, while he drove Philipp to suicide, he didn't kill him.
"Вы, конечно, Авдотья Романовна, слышали тоже у них ...об истории с человеком Филиппом, умершим от истязаний, лет шесть назад, еще во время крепостного права..."
"...принудила или, лучше сказать, склонила его к насильственной смерти беспрерывная система гонений и взысканий господина Свидригайлова."
English:
"You heard, no doubt, Avdotya Romanovna, when you were with
them the story of the servant Philip who died of ill treatment he received six years ago, before the abolition of serfdom."
". . . what drove him, or rather perhaps disposed him, to suicide was the systematic persecution and severity of Mr. Svidrigaïlov."