Formation rule for "∃" in System GHP: "∃ωn+mφ(ω/α)"

Similarly, the fourth formation rule of Grice's natural deduction system concerns the introduction of

∃

and reads:


"If

φ_[n]

is a formula,

∃ω_n+mφ(ω/α)

is a formula"

--- Again, with the caveat, "substitutions are to preserve subscripts".