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Theorem bnj708 29874
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 29868 . 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 29799
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 196  df-an 385  df-bnj17 29800
This theorem is referenced by:  bnj1254  29928  bnj999  30075  bnj1001  30076  bnj1006  30077  bnj1049  30090  bnj1121  30101  bnj1145  30109  bnj1154  30115
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