Theorem pm2.31 511

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 510	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
2	1	biimpri 197	1 ⊢ ((φ ∨ (ψ ∨ χ)) → ((φ ∨ ψ) ∨ χ))

This proof depends on syntax axioms:   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by: (None)