"Love" is being in relation that attracts. Everything loves everything else --like the way company is well loved by misery. It's antithesis is "hate", which is being in relation that repells. Everything also hates everything --like the way misery is repelled by company.
"Definition" is to give form and meaning to something.
"Empirical data" is information gathered through observation, experience and experimentation.
"Evidence" is a bit of information that serves as an indicator of a thing.
"Proof" is that bit of evidence that convinces one of the truth of a thing.
And finally, "existence" is the axiomatic acceptance of being, i.e. to be.
So... the proof that "love" exists is that bit of evidential information that convinces one that being in an attraction relation to other-being should be axiomatically accepted. Well, here's me... There's you...
See, for me that's too far, though I know it's what the OP is asking for. I think the opposite of love is not hate but no love. For me the proof that love exists is that I know when I love and I know when I don't, I have no control over either and hate is not in the equation. Love thy enemy?...impossible, it's not a control thing, it's an emotion.