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Theorem bnj258 31108
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 31107 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
2 df-bnj17 31087 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
31, 2bitri 264 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382  w3a 1070  w-bnj17 31086
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 383  df-3an 1072  df-bnj17 31087
This theorem is referenced by:  bnj707  31157  bnj1019  31182  bnj556  31302  bnj594  31314  bnj1018  31364  bnj1110  31382
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