Ideas from 'Gentzen's Analysis of FirstOrder Proofs' by Dag Prawitz [1974], by Theme Structure
[found in 'A Philosophical Companion to FirstOrder Logic' (ed/tr Hughes,R.I.G.) [Hackett 1993,0872201813]].
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5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13831

Logic is based on transitions between sentences

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13825

Natural deduction introduction rules may represent 'definitions' of logical connectives

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13823

In natural deduction, inferences are atomic steps involving just one logical constant
