Theorem pm2.4 695

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 633	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		id 19	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜓))
3	1, 2	jaoi 636	1 ⊢ ((𝜑 ∨ (𝜑 ∨ 𝜓)) → (𝜑 ∨ 𝜓))

Syntax hints:   → wi 4   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)