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Theorem bnj253 30477
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj253 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))

Proof of Theorem bnj253
StepHypRef Expression
1 bnj248 30473 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 df-3an 1038 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
31, 2bitr4i 267 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1036  w-bnj17 30459
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 386  df-3an 1038  df-bnj17 30460
This theorem is referenced by:  bnj543  30671  bnj558  30680  bnj594  30690  bnj917  30712  bnj929  30714  bnj944  30716  bnj978  30727  bnj998  30734  bnj1006  30737
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