Theorem pm2.53 640

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 789). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.53	⊢ ((φ ∨ ψ) → (¬ φ → ψ))

Proof of Theorem pm2.53

Step	Hyp	Ref	Expression
1		pm2.24 551	. 2 ⊢ (φ → (¬ φ → ψ))
2		ax-1 5	. 2 ⊢ (ψ → (¬ φ → ψ))
3	1, 2	jaoi 635	1 ⊢ ((φ ∨ ψ) → (¬ φ → ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 628

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  ori  641  ord  642  orel1  643  pm2.63  712  notnot2dc  750  dfordc  790  pm5.6r  835  xorbin  1272  19.33b2  1517  onsucelsucexmid  4214  oprabidlem  5476