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Theorem bnj256 31875
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 31869 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 anass 469 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
31, 2bitri 276 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w-bnj17 31855
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 208  df-an 397  df-3an 1081  df-bnj17 31856
This theorem is referenced by:  bnj257  31876  bnj432  31885  bnj543  32064  bnj546  32067  bnj557  32072  bnj916  32104  bnj969  32117  bnj1090  32148  bnj1118  32153  bnj1174  32172
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