Theorem pm5.41 240

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 239	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) ↔ ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2	1	bicomi 123	1 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) ↔ (𝜑 → (𝜓 → 𝜒)))

Syntax hints:   → wi 4   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)