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Theorem bnj253 32001
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj253 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))

Proof of Theorem bnj253
StepHypRef Expression
1 bnj248 31997 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 df-3an 1086 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
31, 2bitr4i 281 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))
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:  bnj543  32192  bnj558  32201  bnj594  32211  bnj917  32233  bnj929  32235  bnj944  32237  bnj978  32248  bnj998  32256  bnj1006  32259
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