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Theorem an13 836
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 834 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜓 ∧ (𝜑𝜒)))
2 anass 679 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
3 ancom 465 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓𝜑)))
41, 2, 33bitr2i 287 1 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383
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 196  df-an 385
This theorem is referenced by:  an31  837  elxp2OLD  5057  elsnxp  5594  elsnxpOLD  5595  dchrelbas3  24763  dfiota3  31200  bj-dfmpt2a  32252  islpln5  33839  islvol5  33883  dibelval3  35454  opeliun2xp  41904
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