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Theorem bnj643 31154
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj643 ((𝜑𝜓𝜒𝜃) → 𝜓)

Proof of Theorem bnj643
StepHypRef Expression
1 bnj291 31114 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
21simprbi 478 1 ((𝜑𝜓𝜒𝜃) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071  w-bnj17 31089
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 1073  df-bnj17 31090
This theorem is referenced by:  bnj706  31159  bnj916  31338  bnj998  31361  bnj1006  31364
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