If someone can prove that one cannot prove from the axioms statement that is opposite to some true statement in the system, does it mean that this system is consistent ? For example, is proving that one cannot prove from the axioms of arithmetic that 0=1 enough for proving arithmetic is consistent ? I thought this is true because of the "principle of explosion".  

Edit: possible proof why it is enough.
If we can prove that within the system we can't prove some concrete statement "A" and "not A" at once than it means that there are no possibility of proving any other opposite statements "B" and "not B" at once, because if there was such a possibility, then by principle of explosion we could both prove "A" and "not A". So from the axioms we can't prove two opposite statements.
Is it valid proof ?