Theorem wl-luk-pm2.21 38193

Description: From a wff and its negation, anything follows. Theorem *2.21 of [WhiteheadRussell] p. 104. Also called the Duns Scotus law. Copy of pm2.21 124 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-luk-pm2.21	⊢ (¬ 𝜑 → (𝜑 → 𝜓))

Proof of Theorem wl-luk-pm2.21

Step	Hyp	Ref	Expression
1		ax-luk3 38177	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))
2	1	wl-luk-com12 38192	1 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))

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

This proof depends on axioms:  ax-mp 5  ax-luk1 38175  ax-luk2 38176  ax-luk3 38177

This theorem is used by:  wl-luk-con1i  38194  wl-luk-ax2  38198