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Theorem bnj334 31299
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 31296 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
2 bnj257 31293 . 2 ((𝜑𝜒𝜃𝜓) ↔ (𝜑𝜒𝜓𝜃))
3 bnj312 31298 . 2 ((𝜑𝜒𝜓𝜃) ↔ (𝜒𝜑𝜓𝜃))
41, 2, 33bitri 289 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜑𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 198  w-bnj17 31272
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 199  df-an 386  df-3an 1110  df-bnj17 31273
This theorem is referenced by:  bnj345  31300  bnj518  31473  bnj916  31520  bnj929  31523
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