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**Ampersand-In (&I)**: If one has available lines, A and B, then one is entitled to write down their conjunction, in one order A&B, or the other order B&A.

**Ampersand-Out (&O):** If one has available a line of the form A&B, then one is entitled to write down either conjunct A or conjunct B.

**Wedge-In (∨I):** If one has available a line A, then one is entitled to write down the disjunction of A with any formula B, in one order AvB, or the other order BvA.

**Wedge-Out (∨O):** If one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the first disjunct, ~A, then one is entitled to write down the second disjunct, B. Likewise, if one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the second disjunct, ~B, then one is entitled to write down the first disjunct, A.

**Double-Arrow-In (↔I):** If one has available a line that is a conditional A→B, and one additionally has available a line that is the converse B→A, then one is entitled to write down either the biconditional A↔B or the biconditional B↔A.

**Double-Arrow-Out (↔O):** If one has available a line of the form A↔B, then one is entitled to write down both the conditional A→B and its converse B→A.

**Arrow-Out (→O)**: If one has available a line of the form A→B, and if one additionally has available a line which is the antecedent A, then one is entitled to write down the consequent B. Likewise, if one has available a line of the form A→B, and if one additionally has available a line which is the negation of the consequent, ~B, then one is entitled to write down the negation of the antecedent, ~A.

**Double Negation (DN):** If one has available a line A, then one is entitled to write down the double-negation ~~A. Similarly, if one has available a line of the form ~~A, then one is entitled to write down the formula A.