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Theorem an42 861
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 860 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜓𝜃)))
2 ancom 464 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32anbi2i 725 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
41, 3bitri 262 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  an43  862  brecop2  7705  supmo  8218  infmo  8261  aceq1  8800  dfiso2  16201  eulerpartlemt0  29564  isbasisrelowllem1  32175  isbasisrelowllem2  32176  ifp1bi  36662
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