1. Z v ~Z tautology 2. Z v (~Z v Q) 1, addition 3. Z v (Z ⊃ Q) 2, material implication 4. [Z v (Z ⊃ Q)] v M 3, addition 5. ~~{[Z v (Z ⊃ Q)] v M} 4, double negation But that does not use indirect proof 1. | ~~~{[Z v (Z ⊃ Q)] v M}I AIP 2. | Edwin