Theorem orel2 680

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		pm2.21 582	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
3	1, 2	jaod 672	1 ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  biorfi  700  pm2.64  750  pm5.71dc  907  ecased  1285  19.30dc  1563  dveeq2  1743  prel12  3615  funun  5058