Metamath Proof Explorer


Theorem wl-luk-pm2.18d

Description: Deduction based on reductio ad absurdum. Copy of pm2.18d with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypothesis wl-luk-pm2.18d.1 ⊢ φ → ¬ ψ → ψ
Assertion wl-luk-pm2.18d ⊢ φ → ψ

Proof

Step Hyp Ref Expression
1 wl-luk-pm2.18d.1 ⊢ φ → ¬ ψ → ψ
2 ax-luk2 ⊢ ¬ ψ → ψ → ψ
3 1 2 wl-luk-syl ⊢ φ → ψ