Theorem pm2.81 824

Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.81	⊢ ((ψ → (χ → θ)) → ((φ ∨ ψ) → ((φ ∨ χ) → (φ ∨ θ))))

Proof of Theorem pm2.81

Step	Hyp	Ref	Expression
1		orim2 814	. 2 ⊢ ((ψ → (χ → θ)) → ((φ ∨ ψ) → (φ ∨ (χ → θ))))
2		pm2.76 821	. 2 ⊢ ((φ ∨ (χ → θ)) → ((φ ∨ χ) → (φ ∨ θ)))
3	1, 2	syl6 29	1 ⊢ ((ψ → (χ → θ)) → ((φ ∨ ψ) → ((φ ∨ χ) → (φ ∨ θ))))

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  df-an 360

This theorem is referenced by: (None)