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Theorem bnj250 31101
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 31087 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
2 3anass 1079 . . 3 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
32anbi1i 602 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃))
4 anass 459 . 2 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
51, 3, 43bitri 286 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382  w3a 1070  w-bnj17 31086
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 383  df-3an 1072  df-bnj17 31087
This theorem is referenced by:  bnj251  31102  bnj252  31103  bnj345  31114
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