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Theorem an3 656
Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010.)
Assertion
Ref Expression
an3 (((𝜑𝜓) ∧ (𝜒𝜃)) → (𝜑𝜃))

Proof of Theorem an3
StepHypRef Expression
1 an43 655 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))
21simplbi 498 1 (((𝜑𝜓) ∧ (𝜒𝜃)) → (𝜑𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  catideu  17384  usgredg2v  27594  prtlem15  36889  clsk1indlem3  41653  poprelb  44976
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