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Theorem bnj290 31287
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj290 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))

Proof of Theorem bnj290
StepHypRef Expression
1 3anrot 1123 . . 3 ((𝜓𝜒𝜃) ↔ (𝜒𝜃𝜓))
21anbi2i 617 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) ↔ (𝜑 ∧ (𝜒𝜃𝜓)))
3 bnj252 31280 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓𝜒𝜃)))
4 bnj252 31280 . 2 ((𝜑𝜒𝜃𝜓) ↔ (𝜑 ∧ (𝜒𝜃𝜓)))
52, 3, 43bitr4i 295 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 385  w3a 1108  w-bnj17 31263
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 31264
This theorem is referenced by:  bnj291  31288  bnj334  31290
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