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Theorem bnj256 31106
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 31100 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 anass 459 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
31, 2bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382  w-bnj17 31086
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 197  df-an 383  df-3an 1072  df-bnj17 31087
This theorem is referenced by:  bnj257  31107  bnj432  31116  bnj543  31295  bnj546  31298  bnj557  31303  bnj916  31335  bnj969  31348  bnj1090  31379  bnj1118  31384  bnj1174  31403
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