Theorem wl-luk-pm2.21 37438

Description: From a wff and its negation, anything follows. Theorem *2.21 of [WhiteheadRussell] p. 104. Also called the Duns Scotus law. Copy of pm2.21 123 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 37422	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))
2	1	wl-luk-com12 37437	1 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 37420  ax-luk2 37421  ax-luk3 37422

This theorem is referenced by:  wl-luk-con1i  37439  wl-luk-ax2  37443