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Theorem an13 645
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 an21 642 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
2 ancom 463 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓𝜑)))
31, 2bitr3i 279 1 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wb 208  wa 398
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 209  df-an 399
This theorem is referenced by:  an31  646  elsnxp  6118  dchrelbas3  25801  dfiota3  33392  bj-dfmpoa  34427  islpln5  36707  islvol5  36751  dibelval3  38319  opeliun2xp  44526
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