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Theorem bnj642 29878
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj642 ((𝜑𝜓𝜒𝜃) → 𝜑)

Proof of Theorem bnj642
StepHypRef Expression
1 bnj446 29842 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜓𝜒𝜃) ∧ 𝜑))
21simprbi 478 1 ((𝜑𝜓𝜒𝜃) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1030  w-bnj17 29811
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 195  df-an 384  df-3an 1032  df-bnj17 29812
This theorem is referenced by:  bnj705  29883  bnj1232  29934  bnj908  30061  bnj1110  30110
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