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Theorem bnj248 30894
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj248 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))

Proof of Theorem bnj248
StepHypRef Expression
1 df-bnj17 30881 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
2 df-3an 1056 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
32anbi1i 731 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
41, 3bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  w3a 1054  w-bnj17 30880
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 385  df-3an 1056  df-bnj17 30881
This theorem is referenced by:  bnj253  30898  bnj256  30900  bnj605  31103  bnj908  31127
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