Natural Deduction Rules |
A B ------ [&I] A & B |
A & B ------ [&E1] A |
A & B ------ [&E2] B |
A ------ [+I1] A + B |
B ------ [+I2] A + B |
A + B A => C B => C ---------------------- [+E] C |
F ---- [Efq] A |
A A => B --------- [=>E] B |
-- A ------- [Raa] A |
The introduction implication Rule =>I is not above. It corresponds
to a Proof Line beginning with the word therefore.
This rule is defined on the syntax page
The conjunction is written &, the disjonction is
written +
I = introduction,
E = elimination,
=>E = modus ponens,
Efq = ex falso quodlibet,
Raa = reductio ad absurdum
In addition to these rules, we define the negation and the equivalence by
-A = A => F
A <=> B = (A => B) & (B => A)
In a proof, one can replace every Formula by an other Formula equal when we replace the Negations and
the Equivalences by their Definitions.
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