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Theorem bnj255 30745
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj255 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓 ∧ (𝜒𝜃)))

Proof of Theorem bnj255
StepHypRef Expression
1 bnj251 30742 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒𝜃))))
2 3anass 1040 . 2 ((𝜑𝜓 ∧ (𝜒𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒𝜃))))
31, 2bitr4i 267 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓 ∧ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1036  w-bnj17 30726
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 30727
This theorem is referenced by:  bnj964  30987  bnj998  31000  bnj1033  31011  bnj1175  31046
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