CONDITIONAL DERIVATIONS

Apart from indirect derivations, we can also make use of hypothetical situations by assuming the antecedent of an intended conditional (the circle in our circle-box game) and demonstrating that the consequent (the box) follows. [We did not have a C int rule before; this gets the same result, however.]

PQC, QRC |- PRC
1. PQC
2. QRC \ show PRC
3. P............hyp
4. Q...........1,3 C elim
5. R...........2,4 C elim
6. PRC.......3-5 hyp elim

Conditional proofs offer us an efficient way to work with relationships such as the following, especially if we use one subordinate proof inside another:

1. PQARC \ show PQRCC
2. P...............hyp
3. ...Q............hyp
4. ...PQA........2,3 A int
5. ...R............1,4 C elim
6. QRC...........3-5 hyp elim
7. PQRCC.......2-6 hyp elim

Remember that you must exit any hypothetical situation that you have proposed. Each hyp must have a corresponding hyp elim.

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