Theorem pm2.64 802

Description: Theorem *2.64 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.64	⊢ ((𝜑 ∨ 𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑))

Proof of Theorem pm2.64

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑))
2		orel2 727	. . 3 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓) → 𝜑))
3	1, 2	jaoi 717	. 2 ⊢ ((𝜑 ∨ ¬ 𝜓) → ((𝜑 ∨ 𝜓) → 𝜑))
4	3	com12 30	1 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)