The given rules of inference for me to use are here: rules of inference

In addition, I was taught the deduction theorem, the ping-pong tautology, specialization and dual specialization (derived rules).

My solution:

Using Deduction Theorem, it suffices if we prove $$A \equiv B, (\forall x)A \vdash (\forall x)B.$$ Hilbert proof:

1) $A ≡ B\quad\langle\text{hypothesis}\rangle$

2) $(\forall x)A\quad\langle\text{hypothesis}\rangle$

3) $A\quad\langle\text{2 + Specialization}\rangle$

I couldn't move past step 3 because I did not know where to go. Any help on this question is appreciated.

Note: This is practice problem is for first year discrete mathematics for engineers course.

  • $\begingroup$ What does that imply? What should be the next step? $\endgroup$ Mar 27, 2020 at 21:00
  • $\begingroup$ The unusal A[x] seems nonsensical. Here is a useful list or rules i.stack.imgur.com/I69BU.png $\endgroup$ Mar 27, 2020 at 21:44

1 Answer 1


I did this, not sure if it's correct or not. enter image description here


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