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Theorem bnj432 30910
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj432 ((𝜑𝜓𝜒𝜃) ↔ ((𝜒𝜃) ∧ (𝜑𝜓)))

Proof of Theorem bnj432
StepHypRef Expression
1 bnj422 30909 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜒𝜃𝜑𝜓))
2 bnj256 30900 . 2 ((𝜒𝜃𝜑𝜓) ↔ ((𝜒𝜃) ∧ (𝜑𝜓)))
31, 2bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜒𝜃) ∧ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  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:  bnj605  31103  bnj600  31115
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