Theorem pm3.22 265

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		pm3.21 264	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑)))
2	1	imp 124	1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∧ 𝜑))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  ancom  266  ancom2s  566  ancom1s  569  eupickb  2126  enq0sym  7499  bj-peano4  15601