Theorem pm2.6 190

Description: Theorem *2.6 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.6	⊢ ((¬ 𝜑 → 𝜓) → ((𝜑 → 𝜓) → 𝜓))

Proof of Theorem pm2.6

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜑 → 𝜓))
2		idd 24	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (𝜓 → 𝜓))
3	1, 2	jad 187	1 ⊢ ((¬ 𝜑 → 𝜓) → ((𝜑 → 𝜓) → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  pm2.61  191