Theorem pm2.21 618

Description: From a wff and its negation, anything is true. Theorem *2.21 of [WhiteheadRussell] p. 104. Also called the Duns Scotus law. (Contributed by Mario Carneiro, 12-May-2015.)

Assertion

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

Proof of Theorem pm2.21

Step	Hyp	Ref	Expression
1		ax-in2 616	1 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-in2 616

This theorem is referenced by:  pm2.21d  620  pm2.24  622  pm2.24i  624  pm2.21i  647  jarl  659  mtt  686  orel2  727  imorri  750  pm2.42  778  pm2.18dc  856  simplimdc  861  peircedc  915  pm4.82  952  pm5.71dc  963  dedlemb  972  mo2n  2070  exmodc  2092  exmonim  2093  nrexrmo  2715  opthpr  3798  0neqopab  5963  0mnnnnn0  9272  flqeqceilz  10389