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Theorem bnj268 31974
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj268 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜓𝜃))

Proof of Theorem bnj268
StepHypRef Expression
1 3ancomb 1095 . . 3 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
21anbi1i 625 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑𝜒𝜓) ∧ 𝜃))
3 df-bnj17 31952 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
4 df-bnj17 31952 . 2 ((𝜑𝜒𝜓𝜃) ↔ ((𝜑𝜒𝜓) ∧ 𝜃))
52, 3, 43bitr4i 305 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 208  wa 398  w3a 1083  w-bnj17 31951
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 209  df-an 399  df-3an 1085  df-bnj17 31952
This theorem is referenced by:  bnj543  32160  bnj929  32203  bnj1110  32249
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