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Theorem bnj258 33548
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj258 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))

Proof of Theorem bnj258
StepHypRef Expression
1 bnj257 33547 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
2 df-bnj17 33527 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
31, 2bitri 274 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396  w3a 1087  w-bnj17 33526
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 206  df-an 397  df-3an 1089  df-bnj17 33527
This theorem is referenced by:  bnj707  33595  bnj1019  33619  bnj556  33740  bnj594  33752  bnj1018g  33803  bnj1018  33804  bnj1110  33822
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