Theorem pm2.82 825

Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.82	⊢ (((φ ∨ ψ) ∨ χ) → (((φ ∨ ¬ χ) ∨ θ) → ((φ ∨ ψ) ∨ θ)))

Proof of Theorem pm2.82

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ ((φ ∨ ψ) → ((φ ∨ ¬ χ) → (φ ∨ ψ)))
2		pm2.24 101	. . . 4 ⊢ (χ → (¬ χ → ψ))
3	2	orim2d 813	. . 3 ⊢ (χ → ((φ ∨ ¬ χ) → (φ ∨ ψ)))
4	1, 3	jaoi 368	. 2 ⊢ (((φ ∨ ψ) ∨ χ) → ((φ ∨ ¬ χ) → (φ ∨ ψ)))
5	4	orim1d 812	1 ⊢ (((φ ∨ ψ) ∨ χ) → (((φ ∨ ¬ χ) ∨ θ) → ((φ ∨ ψ) ∨ θ)))

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  df-an 360

This theorem is referenced by: (None)