I have hard time determining whether the below argument is valid:
(P1) Nobody ever plays with a bear.
(P2) Bob plays with a bear.
(C) Therefore, bears are friendly.
I think this argument is valid. Suppose this argument is invalid. Then the premises P1 and P2 are true while the conclusion C is false. We get a contradiction if both P1 and P2 are jointly true. So, the argument must be valid, by the law of excluded middle.
Is my reasoning correct?