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Theorem bnj251 30528
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj251 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒𝜃))))

Proof of Theorem bnj251
StepHypRef Expression
1 bnj250 30527 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
2 anass 680 . . 3 (((𝜓𝜒) ∧ 𝜃) ↔ (𝜓 ∧ (𝜒𝜃)))
32anbi2i 729 . 2 ((𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒𝜃))))
41, 3bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w-bnj17 30512
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 386  df-3an 1038  df-bnj17 30513
This theorem is referenced by:  bnj255  30531  bnj535  30721  bnj570  30736  bnj953  30770  bnj1110  30811
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