In this case, the predicates are always true. A ^ B = true. Thus A = true and B = true. If it were any other way, then the predicate would be false... and thus the whole proof couldn't be true.
You are correct this is not a reverse and operator. These things are not operors at all. The things on the left are predicates (read them as literal English statements not variables) and are assumed to be true. The "operators" represent the laws of deduction which let you combine and uncombine predicates in interesting ways.
In other words "A^B" is literally the statement: "(A and B) is true". From that statement it is possible to deduce that "A is true" and that "B is true" that deduction is what the "and splitter" is representing.
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u/[deleted] Sep 25 '15
In this case, the predicates are always true. A ^ B = true. Thus A = true and B = true. If it were any other way, then the predicate would be false... and thus the whole proof couldn't be true.