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Theorem bnj252 34696
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj252 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓𝜒𝜃)))

Proof of Theorem bnj252
StepHypRef Expression
1 bnj250 34694 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
2 df-3an 1088 . . 3 ((𝜓𝜒𝜃) ↔ ((𝜓𝜒) ∧ 𝜃))
32anbi2i 623 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
41, 3bitr4i 278 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395  w3a 1086  w-bnj17 34679
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 207  df-an 396  df-3an 1088  df-bnj17 34680
This theorem is referenced by:  bnj290  34703  bnj563  34736  bnj919  34760  bnj976  34770  bnj543  34886  bnj570  34898  bnj594  34905  bnj916  34926  bnj917  34927  bnj964  34936  bnj983  34944  bnj984  34945  bnj998  34950  bnj999  34951  bnj1021  34959  bnj1083  34971  bnj1450  35043
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