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Theorem bnj250 31218
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj250 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))

Proof of Theorem bnj250
StepHypRef Expression
1 df-bnj17 31204 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
2 3anass 1116 . . 3 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
32anbi1i 617 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃))
4 anass 460 . 2 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
51, 3, 43bitri 288 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 197  wa 384  w3a 1107  w-bnj17 31203
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 198  df-an 385  df-3an 1109  df-bnj17 31204
This theorem is referenced by:  bnj251  31219  bnj252  31220  bnj345  31231
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