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Theorem bnj422 31115
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
bnj422 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜃𝜑𝜓))

Proof of Theorem bnj422
StepHypRef Expression
1 bnj345 31114 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜃𝜑𝜓𝜒))
2 bnj345 31114 . 2 ((𝜃𝜑𝜓𝜒) ↔ (𝜒𝜃𝜑𝜓))
31, 2bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜃𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  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:  bnj432  31116  bnj535  31292  bnj558  31304
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