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Theorem an13 638
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 636 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜓 ∧ (𝜑𝜒)))
2 anass 461 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
3 ancom 453 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜒 ∧ (𝜓𝜑)))
41, 2, 33bitr2i 291 1 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 385
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 199  df-an 386
This theorem is referenced by:  an31  639  elsnxp  5894  dchrelbas3  25312  dfiota3  32535  bj-dfmpt2a  33556  islpln5  35548  islvol5  35592  dibelval3  37160  opeliun2xp  42898
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