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Theorem bnj708 31368
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 31362 . 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 31297
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 199  df-an 387  df-bnj17 31298
This theorem is referenced by:  bnj1254  31422  bnj999  31569  bnj1001  31570  bnj1006  31571  bnj1049  31584  bnj1121  31595  bnj1145  31603  bnj1154  31609
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