Now, fulfils (α) and (β). For (α) being the complex expression , is a case of the form , and (β) we have, by (c) above, and by (a) .
To obtain the strictest development of the proof we have only to write for and for all through the preceding argument.
Permutation, |
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Dem.: Prop. , Id., and Rule.
Tautology, |
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i.e.
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Dem.: Id. , Perm., and Rule.
Addition, |
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Dem.: By Perm. (twice), (a)
By Prop. Id.[1],
By Perm., result.
Return from Generalised Implication to .
Lemma, |
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Dem.: By Perm. (twice), (a)
By Prop. (a),
Write for : by Id. and Perm. (twice), result.
- ↑ (a) means the use of the Rule to pass from to in .