I have these formulas of CL:
(a) ∀xP(x,x)
(b) ∀x∀y∀z(P(x,y)∧P(y,z) → P(x,z))
(c) ∀x∀y(P(x,y) → ¬P(y,x)
and I have been trying to prove weather (a),(b) ⊨ (c). First I would use ∀l and then my question is, can I apply this rule for every single ∀x (y or z) and then just have many eigenvariables or is there another way?
If anyone knows of exercises similar to this for practice that would be very helpful