Metamath Proof Explorer


Theorem bj-eximALT

Description: Alternate proof of exim directly from alim by using df-ex (using duality of A. and E. . (Contributed by BJ, 9-Dec-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion bj-eximALT x φ ψ x φ x ψ

Proof

Step Hyp Ref Expression
1 con3 φ ψ ¬ ψ ¬ φ
2 1 alimi x φ ψ x ¬ ψ ¬ φ
3 alim x ¬ ψ ¬ φ x ¬ ψ x ¬ φ
4 con3 x ¬ ψ x ¬ φ ¬ x ¬ φ ¬ x ¬ ψ
5 2 3 4 3syl x φ ψ ¬ x ¬ φ ¬ x ¬ ψ
6 df-ex x φ ¬ x ¬ φ
7 df-ex x ψ ¬ x ¬ ψ
8 5 6 7 3imtr4g x φ ψ x φ x ψ