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Theorem an42 901
Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
an42 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))

Proof of Theorem an42
StepHypRef Expression
1 an4 900 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜓𝜃)))
2 ancom 465 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32anbi2i 732 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
41, 3bitri 264 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  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 197  df-an 385
This theorem is referenced by:  an43  902  brecop2  8011  supmo  8526  infmo  8569  aceq1  9151  dfiso2  16654  eulerpartlemt0  30762  isbasisrelowllem1  33533  isbasisrelowllem2  33534  ifp1bi  38368
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