Theorem pm2.86 106

Description: Converse of axiom ax-2 7. Theorem *2.86 of [WhiteheadRussell] p. 108. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Assertion

Ref	Expression
pm2.86	⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))

Proof of Theorem pm2.86

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2	1	pm2.86d 105	1 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  pm2.86iALT  108  imdi  377