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Theorem bnj334 30753
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj334 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜑𝜓𝜃))

Proof of Theorem bnj334
StepHypRef Expression
1 bnj290 30750 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
2 bnj257 30747 . 2 ((𝜑𝜒𝜃𝜓) ↔ (𝜑𝜒𝜓𝜃))
3 bnj312 30752 . 2 ((𝜑𝜒𝜓𝜃) ↔ (𝜒𝜑𝜓𝜃))
41, 2, 33bitri 286 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜑𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  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:  bnj345  30754  bnj518  30930  bnj916  30977  bnj929  30980
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