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Theorem bnj256 31980
 Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj256 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))

Proof of Theorem bnj256
StepHypRef Expression
1 bnj248 31974 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 anass 471 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
31, 2bitri 277 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 208   ∧ wa 398   ∧ w-bnj17 31960 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 209  df-an 399  df-3an 1085  df-bnj17 31961 This theorem is referenced by:  bnj257  31981  bnj432  31990  bnj543  32169  bnj546  32172  bnj557  32177  bnj916  32209  bnj969  32222  bnj1090  32255  bnj1118  32260  bnj1174  32279
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