particle physics - How did Paul Dirac predict the existence of antiproton?

The existence of the antiproton with -1 electric charge, opposite to the +1 electric charge of the proton, was predicted by Paul Dirac in his 1933 Nobel Prize lecture.

Question. How did Paul Dirac predict existence of antiproton?

Answer

You'll find Dirac's 1933 Nobel lecture on the Nobelprize.org website. The pdf is quite brief (5 pages long) and speaks on the antiproton at the end (p4). The argument is the following :

In any case I think it is probable that negative protons can exist, since as far as the theory is yet definite, there is a complete and perfect symmetry between positive and negative electric charge, and if this symmetry is really fundamental in nature, it must be possible to reverse the charge on any kind of particle.

In short, the particle-antiparticle symmetry seems to be a law of nature, so the proton should also have an an anti-proton partner.

Edited to expand below

@ANKU's answer above is the answer to the question "How did Dirac predict the existence of antimatter", and this work was done for the electron (or the positron). Once the positron has been predicted and and observed, came the intuition that this symmetry was much more general. However, in 1933, Dirac didn't think that this theory could be directly applied to protons. To quote his Nobel lecture :

The theory of electrons and positrons which I have just outlined is a self- consistent theory which fits the experimental facts so far as is yet known. One would like to have an equally satisfactory theory for protons. One might perhaps think that the same theory could be applied to protons. This would require the possibility of existence of negatively charged protons forming a mirror-image of the usual positively charged ones. There is, however, some recent experimental evidence obtained by Stern about the spin magnetic moment of the proton, which conflicts with this theory for the proton. As the proton is so much heavier than the electron, it is quite likely that it requires some more complicated theory, though one cannot at the present time say what this theory is.