Theorem pm2.63 790

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		pm2.53 712	. 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))
2		idd 21	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 → 𝜓))
3	1, 2	jaod 707	1 ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜑 ∨ 𝜓) → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)