Theorem wl-pm2.18d 32424

Description: Deduction based on reductio ad absurdum. Copy of pm2.18d 123 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-pm2.18d.1	⊢ (𝜑 → (¬ 𝜓 → 𝜓))

Assertion

Ref	Expression
wl-pm2.18d	⊢ (𝜑 → 𝜓)

Proof of Theorem wl-pm2.18d

Step	Hyp	Ref	Expression
1		wl-pm2.18d.1	. 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜓))
2		ax-luk2 32418	. 2 ⊢ ((¬ 𝜓 → 𝜓) → 𝜓)
3	1, 2	wl-syl 32422	1 ⊢ (𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418

This theorem is referenced by:  wl-con4i  32425  wl-mpi  32428  wl-con1i  32436  wl-ja  32437