Theorem orel1 371

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)

Assertion

Ref	Expression
orel1	⊢ (¬ φ → ((φ ∨ ψ) → ψ))

Proof of Theorem orel1

Step	Hyp	Ref	Expression
1		pm2.53 362	. 2 ⊢ ((φ ∨ ψ) → (¬ φ → ψ))
2	1	com12 27	1 ⊢ (¬ φ → ((φ ∨ ψ) → ψ))

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

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

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

This theorem is referenced by:  pm2.25  393  biorf  394  euor2  2272  nndisjeq  4429  nnceleq  4430  sfinltfin  4535  sfin111  4536  phialllem1  4616  xpcan  5057  funun  5146  enprmaplem3  6078