Theorem pm2.64 826

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		orel2 397	. . 3 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓) → 𝜑))
2	1	jao1i 821	. 2 ⊢ ((𝜑 ∨ ¬ 𝜓) → ((𝜑 ∨ 𝜓) → 𝜑))
3	2	com12 32	1 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

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

This theorem depends on definitions:  df-bi 196  df-or 384

This theorem is referenced by:  hirstL-ax3  39708