I see what I was doing here. The law of excluded middle is equivalent to the law of non-contradiction. Probably why I had the two confused. Example in sentential logic:

1. ¬(p∧¬p) (law of non-contradiction)
2. ¬p∨¬¬p | 1, de morgan's
3. ¬p∨p | 2, double negation
4. p∨¬p | 3, commutation (law of excluded middle)