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Theorem an42 654
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 653 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜓𝜃)))
2 ancom 461 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32anbi2i 623 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
41, 3bitri 274 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396
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 206  df-an 397
This theorem is referenced by:  an43  655  an33rean  1482  brecop2  8588  supmo  9199  infmo  9242  aceq1  9861  dfiso2  17472  eulerpartlemt0  32322  isbasisrelowllem1  35512  isbasisrelowllem2  35513  ifp1bi  41077
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