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Theorem an13 839
 Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Assertion
Ref Expression
an13 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))

Proof of Theorem an13
StepHypRef Expression
1 an12 837 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜓 ∧ (𝜑𝜒)))
2 anass 680 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
3 ancom 466 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓𝜑)))
41, 2, 33bitr2i 288 1 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   ∧ wa 384 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 197  df-an 386 This theorem is referenced by:  an31  840  elxp2OLD  5103  elsnxp  5646  elsnxpOLD  5647  dchrelbas3  24897  dfiota3  31725  bj-dfmpt2a  32747  islpln5  34340  islvol5  34384  dibelval3  35955  opeliun2xp  41429
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