Metamath Proof Explorer

Theorem bj-exalimi

Description: An inference for distributing quantifiers over a nested implication. The canonical derivation from its closed form bj-exalim (using mpg ) has fewer essential steps, but more steps in total (yielding a longer compressed proof). (Almost) the general statement that speimfw proves. (Contributed by BJ, 29-Sep-2019)

Ref Expression
Hypothesis bj-exalimi.1 φ ψ χ
Assertion bj-exalimi x φ x ψ x χ


Step Hyp Ref Expression
1 bj-exalimi.1 φ ψ χ
2 1 com12 ψ φ χ
3 2 aleximi x ψ x φ x χ
4 3 com12 x φ x ψ x χ