We can now recognize the difference of partials as a (scalar) triple product : ∂ ∂ P v ∂ ∂ u − − ∂ ∂ P u ∂ ∂ v = ∂ ∂ ψ ψ ∂ ∂ v ⋅ ⋅ ( ∇ ∇ × × F ) × × ∂ ∂ ψ ψ ∂ ∂ u = ( ∇ ∇ × × F ) ⋅ ⋅ ∂ ∂ ψ ψ ∂ ∂ u × × ∂ ∂ ψ ψ ∂ ∂ v