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Theorem bnj291 32008
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 32007 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
2 df-bnj17 31984 . 2 ((𝜑𝜒𝜃𝜓) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
31, 2bitri 278 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  w3a 1084  w-bnj17 31983
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 210  df-an 400  df-3an 1086  df-bnj17 31984
This theorem is referenced by:  bnj643  32047  bnj938  32236  bnj944  32237
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