Theorem pm2.85 826

Description: Theorem *2.85 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)

Assertion

Ref	Expression
pm2.85	⊢ (((φ ∨ ψ) → (φ ∨ χ)) → (φ ∨ (ψ → χ)))

Proof of Theorem pm2.85

Step	Hyp	Ref	Expression
1		orimdi 820	. 2 ⊢ ((φ ∨ (ψ → χ)) ↔ ((φ ∨ ψ) → (φ ∨ χ)))
2	1	biimpri 197	1 ⊢ (((φ ∨ ψ) → (φ ∨ χ)) → (φ ∨ (ψ → χ)))

Syntax hints:   → 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: (None)