SLR parse table and unambiguity
As said in the comment by Yuval, an SLR parse table with no conflicts (or parsing deterministic finite automaton) for a particular grammar implies that the grammar is unambiguous.

In fact, that is true for most if not all popular parsing methods.


LL(k) 
LR(k)
SLR(k)
LALR(k)




Here is the sketch of a proof for all parsing methods. A parse table or a parsing finite automaton specifies an algorithm to produce all leftmost derivations (or rightmost derivations) of the input sentence. If there is no conflict in the parse table or the finite automaton is deterministic, only one derivation can be generated. That means the grammar is unambiguous. 

Note for a given sentence, there is only one leftmost derivation is equivalent to there is only one rightmost derivation.