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Theorem bnj252 30897
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 30895 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
2 df-3an 1056 . . 3 ((𝜓𝜒𝜃) ↔ ((𝜓𝜒) ∧ 𝜃))
32anbi2i 730 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
41, 3bitr4i 267 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓𝜒𝜃)))
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:  bnj290  30904  bnj563  30939  bnj919  30963  bnj976  30974  bnj543  31089  bnj570  31101  bnj594  31108  bnj916  31129  bnj917  31130  bnj964  31139  bnj983  31147  bnj984  31148  bnj998  31152  bnj999  31153  bnj1021  31160  bnj1083  31172  bnj1450  31244
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