# Natural deduction proof - is this correct? I don't know of any means to check my work, can anyone point out if they're any mistakes?

• It is prefered that you type things out rather than use an outside link. Text is searchable, and links may disappear. – Graham Kemp Nov 23 '18 at 3:27

## 1 Answer

Yes.   You are putting the deductions before their sub-proofs and the naming convention is not quite what I'm used to, but that looks okay.

To check, in my prefered format that would be:

$$\small\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline #2\end{array}}\fitch{1.~\lnot (p\to q)\qquad\textsf{Premise}}{\fitch{2.~\lnot(p\land\lnot q)\qquad\textsf{Assumption}}{3.~\lnot(p\to q)\qquad\textsf{Reiteration (1)}}\\4.~ \lnot(p\land\lnot q)\to\lnot(p\to q)\qquad\textsf{Conditional Introduction (2-3)}\\\fitch{5.~\lnot(p\land\lnot q)\qquad\textsf{Assumption}}{\fitch{6.~p\qquad\textsf{Assumption}}{\fitch{7.~\lnot q\qquad\textsf{Assumption}}{8.~p\land\lnot q\qquad\textsf{Conjunction Introduction (6,7)}}\\9.~\lnot q\to( p\land\lnot q)\qquad\textsf{Conditional Introduction (7-8)}\\\fitch{10.~\lnot q\qquad\textsf{Assumption}}{11.~\lnot (p\land\lnot q)\qquad\textsf{Reiteration (5)}}\\12.~\lnot q\to\lnot(p\land\lnot q)\qquad\textsf{Conditional Introduction (10-11)}\\13.~\lnot\lnot q\qquad\textsf{Negation Introduction (9,12)}\\14.~q\qquad\textsf{Double Negation Elimination (13)}}\\15.~p\to q\qquad\textsf{Conditional Introduction (6-14)}}\\16.~\lnot(p\land\lnot q)\to (p\to q)\qquad\textsf{Conditional Introduction (5-15)}\\17.~\lnot\lnot(p\land\lnot q)\qquad\textsf{Negation Introduction (4,16)}\\18.~p\land\lnot q\qquad\textsf{Double Negation Elimination (17)}\\\blacksquare}$$