Theorem wl-luk-pm2.18d 38100

Description: Deduction based on reductio ad absurdum. Copy of pm2.18d 128 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

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

Assertion

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

Proof of Theorem wl-luk-pm2.18d

Step	Hyp	Ref	Expression
1		wl-luk-pm2.18d.1	. 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜓))
2		ax-luk2 38094	. 2 ⊢ ((¬ 𝜓 → 𝜓) → 𝜓)
3	1, 2	wl-luk-syl 38098	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38093  ax-luk2 38094

This theorem is used by:  wl-luk-con4i  38101  wl-luk-mpi  38104  wl-luk-con1i  38112  wl-luk-ja  38113