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Theorem bnj708 32736
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj708.1 (𝜃𝜏)
Assertion
Ref Expression
bnj708 ((𝜑𝜓𝜒𝜃) → 𝜏)

Proof of Theorem bnj708
StepHypRef Expression
1 bnj645 32730 . 2 ((𝜑𝜓𝜒𝜃) → 𝜃)
2 bnj708.1 . 2 (𝜃𝜏)
31, 2syl 17 1 ((𝜑𝜓𝜒𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w-bnj17 32665
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 206  df-an 397  df-bnj17 32666
This theorem is referenced by:  bnj1254  32789  bnj999  32938  bnj1001  32939  bnj1006  32940  bnj1049  32954  bnj1121  32965  bnj1145  32973  bnj1154  32979
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