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Theorem an42 656
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 655 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜓𝜃)))
2 ancom 464 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32anbi2i 625 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
41, 3bitri 278 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  an43  657  an33rean  1480  brecop2  8366  supmo  8892  infmo  8935  aceq1  9520  dfiso2  17021  eulerpartlemt0  31635  isbasisrelowllem1  34656  isbasisrelowllem2  34657  ifp1bi  40017
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