Theorem pm5.14 856

Description: Theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.14	⊢ ((φ → ψ) ∨ (ψ → χ))

Proof of Theorem pm5.14

Step	Hyp	Ref	Expression
1		ax-1 6	. . . 4 ⊢ (ψ → (φ → ψ))
2	1	con3i 127	. . 3 ⊢ (¬ (φ → ψ) → ¬ ψ)
3	2	pm2.21d 98	. 2 ⊢ (¬ (φ → ψ) → (ψ → χ))
4	3	orri 365	1 ⊢ ((φ → ψ) ∨ (ψ → χ))

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

This theorem is referenced by:  pm5.13  857