Theorem pm3.22 436

Description: Theorem *3.22 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)

Assertion

Ref	Expression
pm3.22	⊢ ((φ ∧ ψ) → (ψ ∧ φ))

Proof of Theorem pm3.22

Step	Hyp	Ref	Expression
1		pm3.21 435	. 2 ⊢ (φ → (ψ → (ψ ∧ φ)))
2	1	imp 418	1 ⊢ ((φ ∧ ψ) → (ψ ∧ φ))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  ancom  437  ancom2s  777  ancom1s  780  eupickb  2269