Theorem pm2.63 955

Description: Theorem *2.63 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.63	⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜑 ∨ 𝜓) → 𝜓))

Proof of Theorem pm2.63

Step	Hyp	Ref	Expression
1		pm2.53 865	. 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))
2		idd 25	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 → 𝜓))
3	1, 2	jaod 873	1 ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜑 ∨ 𝜓) → 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

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

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  poimirlem31  38570