Symbolic Logic, Irving M. Copi, Prentice Hall, 5th edition, 1979, p. 149, problem 1

We are asked to prove the validity of the following argument:

The architect who designed Tappan Hall designs only office buildings. Therefore, Tappan Hall is an office building.

The proof is straightforward. The thing to watch out for in symbolizing the premise is 'only'. 'he designs only office buildings' translates as 'if z is not an office building then he did not desing it' or, by contraposition, 'if he designs it then it is an office building'.

1. (∃x){Ax • Dxt • (y)[(Ay • Dyt) ⊃y = x] • (z)(Dxz ⊃Oz)}
2. ∴Ot
3. Am • Dmt • (y)[(Ay • Dyt) ⊃y = m] • (z)(Dmz ⊃Oz)} / 1EI x/m
4. Dmt / 3Simp.
5. (z)(Dmz ⊃Oz) / 3Simp.
6. Dmt ⊃Ot / 5UI z/t
7. Ot / 4,6MP