Theorem pm2.8 823

Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)

Assertion

Ref	Expression
pm2.8	⊢ ((φ ∨ ψ) → ((¬ ψ ∨ χ) → (φ ∨ χ)))

Proof of Theorem pm2.8

Step	Hyp	Ref	Expression
1		pm2.53 362	. . 3 ⊢ ((φ ∨ ψ) → (¬ φ → ψ))
2	1	con1d 116	. 2 ⊢ ((φ ∨ ψ) → (¬ ψ → φ))
3	2	orim1d 812	1 ⊢ ((φ ∨ ψ) → ((¬ ψ ∨ χ) → (φ ∨ χ)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by: (None)