Theorem pm2.4 768

Description: Theorem *2.4 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.4	⊢ ((𝜑 ∨ (𝜑 ∨ 𝜓)) → (𝜑 ∨ 𝜓))

Proof of Theorem pm2.4

Step	Hyp	Ref	Expression
1		orc 702	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		id 19	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜓))
3	1, 2	jaoi 706	1 ⊢ ((𝜑 ∨ (𝜑 ∨ 𝜓)) → (𝜑 ∨ 𝜓))

Syntax hints:   → 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-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)