Theorem orel2 372

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)

Assertion

Ref	Expression
orel2	⊢ (¬ φ → ((ψ ∨ φ) → ψ))

Proof of Theorem orel2

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (¬ φ → (ψ → ψ))
2		pm2.21 100	. 2 ⊢ (¬ φ → (φ → ψ))
3	1, 2	jaod 369	1 ⊢ (¬ φ → ((ψ ∨ φ) → ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  biorfi  396  pm2.64  764  pm2.74  819  pm5.71  902  nndisjeq  4430  xpcan2  5059  funun  5147  enadjlem1  6060  enadj  6061