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Theorem bnj253 31873
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj253 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))

Proof of Theorem bnj253
StepHypRef Expression
1 bnj248 31869 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 df-3an 1081 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
31, 2bitr4i 279 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w3a 1079  w-bnj17 31855
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 208  df-an 397  df-3an 1081  df-bnj17 31856
This theorem is referenced by:  bnj543  32064  bnj558  32073  bnj594  32083  bnj917  32105  bnj929  32107  bnj944  32109  bnj978  32120  bnj998  32127  bnj1006  32130
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