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Theorem bnj721 31927
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj721.1 ((𝜑𝜓𝜒) → 𝜏)
Assertion
Ref Expression
bnj721 ((𝜑𝜓𝜒𝜃) → 𝜏)

Proof of Theorem bnj721
StepHypRef Expression
1 bnj658 31921 . 2 ((𝜑𝜓𝜒𝜃) → (𝜑𝜓𝜒))
2 bnj721.1 . 2 ((𝜑𝜓𝜒) → 𝜏)
31, 2syl 17 1 ((𝜑𝜓𝜒𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079  w-bnj17 31855
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 208  df-an 397  df-bnj17 31856
This theorem is referenced by:  bnj570  32076  bnj594  32083  bnj999  32128  bnj1093  32149
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