Theorem pm5.41 353

Description: Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 12-Oct-2012.)

Assertion

Ref	Expression
pm5.41	⊢ (((φ → ψ) → (φ → χ)) ↔ (φ → (ψ → χ)))

Proof of Theorem pm5.41

Step	Hyp	Ref	Expression
1		imdi 352	. 2 ⊢ ((φ → (ψ → χ)) ↔ ((φ → ψ) → (φ → χ)))
2	1	bicomi 193	1 ⊢ (((φ → ψ) → (φ → χ)) ↔ (φ → (ψ → χ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by: (None)