Turkhan Badalov

Another note regarding proving a statement in the form P->Q really means to show it is impossible for Q to be false when P is true. This could be achieved by two ways: 1. Deduction - what was done in the original post. 2. By contradiction

I want to add a few things here, when talking about tautology or soundness - we have to clearly separate argument forms from specific arguments. Tautology is a property of a form. Indeed, tautology means always true but for forms, but when we are talking about concrete statements, it is what @ryang is saying that a statement can be true in our universe but false in some other. That being said, to say that P implies Q (note, this is a form) means P -> Q is a tautology.