Metamath Proof Explorer

Theorem bj-exlimg

Description: The general form of the *exlim* family of theorems: if ph is substituted for ps , then the antecedent expresses a form of nonfreeness of x in ph , so the theorem means that under a nonfreeness condition in a consequent, one can deduce from the universally quantified implication an implication where the antecedent is existentially quantified. Dual of bj-alrimg . (Contributed by BJ, 9-Dec-2023)

Ref Expression
Assertion bj-exlimg x φ ψ x χ φ x χ ψ


Step Hyp Ref Expression
1 bj-sylget x χ φ x φ ψ x χ ψ
2 1 com12 x φ ψ x χ φ x χ ψ