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Theorem bnj645 29868
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj645 ((𝜑𝜓𝜒𝜃) → 𝜃)

Proof of Theorem bnj645
StepHypRef Expression
1 df-bnj17 29800 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
21simprbi 479 1 ((𝜑𝜓𝜒𝜃) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1031  w-bnj17 29799
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 196  df-an 385  df-bnj17 29800
This theorem is referenced by:  bnj708  29874  bnj908  30049  bnj929  30054  bnj964  30061  bnj1110  30098
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