[kevinzz]

In Lean you could do

  theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p := by cc

for a tactic proof and

  theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p := λ ⟨h,j⟩,⟨j,h⟩

for a term proof (just write down the function).