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Theorem bnj252 30473
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 30471 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
2 df-3an 1038 . . 3 ((𝜓𝜒𝜃) ↔ ((𝜓𝜒) ∧ 𝜃))
32anbi2i 729 . 2 ((𝜑 ∧ (𝜓𝜒𝜃)) ↔ (𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)))
41, 3bitr4i 267 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑 ∧ (𝜓𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1036  w-bnj17 30456
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 30457
This theorem is referenced by:  bnj290  30480  bnj563  30518  bnj919  30542  bnj976  30553  bnj543  30668  bnj570  30680  bnj594  30687  bnj916  30708  bnj917  30709  bnj964  30718  bnj983  30726  bnj984  30727  bnj998  30731  bnj999  30732  bnj1021  30739  bnj1083  30751  bnj1450  30823
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