Counting Game

For all R { {for any (coded) formula [ψ] and any variable assignment t (R([ψ],t) ↔ (([ψ] = "xi ∈ xj" ∧ t(xi) ∈ t(xj)) ∨ ([ψ] = "xi = xj" ∧ t(xi) = t(xj)) ∨ ([ψ] = "(∼θ)" ∧ ∼R([θ],t)) ∨ ([ψ] = "(θ∧ξ)" ∧ R([θ],t) ∧ R([ξ],t)) ∨ ([ψ] = "∃xi (θ)" and, for some an xi-variant t' of t, R([θ],t')) )} → R([φ],s)}

I've gotta mention that I don't understand this, I saw it in a Numberphile video