Theorem pm2.74 819

Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm2.74	⊢ ((ψ → φ) → (((φ ∨ ψ) ∨ χ) → (φ ∨ χ)))

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		orel2 372	. . 3 ⊢ (¬ ψ → ((φ ∨ ψ) → φ))
2		ax-1 6	. . 3 ⊢ (φ → ((φ ∨ ψ) → φ))
3	1, 2	ja 153	. 2 ⊢ ((ψ → φ) → ((φ ∨ ψ) → φ))
4	3	orim1d 812	1 ⊢ ((ψ → φ) → (((φ ∨ ψ) ∨ χ) → (φ ∨ 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  df-an 360

This theorem is referenced by: (None)