Theorem pm2.37 817

Description: Theorem *2.37 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.)

Assertion

Ref	Expression
pm2.37	⊢ ((ψ → χ) → ((ψ ∨ φ) → (φ ∨ χ)))

Proof of Theorem pm2.37

Step	Hyp	Ref	Expression
1		pm2.38 815	. 2 ⊢ ((ψ → χ) → ((ψ ∨ φ) → (χ ∨ φ)))
2		pm1.4 375	. 2 ⊢ ((χ ∨ φ) → (φ ∨ χ))
3	1, 2	syl6 29	1 ⊢ ((ψ → χ) → ((ψ ∨ φ) → (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)