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Theorem bnj291 30519
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj291 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))

Proof of Theorem bnj291
StepHypRef Expression
1 bnj290 30518 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
2 df-bnj17 30495 . 2 ((𝜑𝜒𝜃𝜓) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
31, 2bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1036  w-bnj17 30494
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 30495
This theorem is referenced by:  bnj643  30562  bnj938  30750  bnj944  30751
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