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Theorem bnj446 32044
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj446 ((𝜑𝜓𝜒𝜃) ↔ ((𝜓𝜒𝜃) ∧ 𝜑))

Proof of Theorem bnj446
StepHypRef Expression
1 bnj345 32041 . 2 ((𝜓𝜒𝜃𝜑) ↔ (𝜑𝜓𝜒𝜃))
2 df-bnj17 32014 . 2 ((𝜓𝜒𝜃𝜑) ↔ ((𝜓𝜒𝜃) ∧ 𝜑))
31, 2bitr3i 280 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜓𝜒𝜃) ∧ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  w3a 1084  w-bnj17 32013
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 32014
This theorem is referenced by:  bnj642  32076  bnj667  32080  bnj594  32241
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