Theorem pm2.31 685

Description: Theorem *2.31 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.31	⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → ((𝜑 ∨ 𝜓) ∨ 𝜒))

Proof of Theorem pm2.31

Step	Hyp	Ref	Expression
1		orass 684	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
2	1	biimpri 124	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → ((𝜑 ∨ 𝜓) ∨ 𝜒))

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)