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Theorem syl8ib 164
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.)
Hypotheses
Ref Expression
syl8ib.1 (𝜑 → (𝜓 → (𝜒𝜃)))
syl8ib.2 (𝜃𝜏)
Assertion
Ref Expression
syl8ib (𝜑 → (𝜓 → (𝜒𝜏)))

Proof of Theorem syl8ib
StepHypRef Expression
1 syl8ib.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 syl8ib.2 . . 3 (𝜃𝜏)
32biimpi 118 . 2 (𝜃𝜏)
41, 3syl8 70 1 (𝜑 → (𝜓 → (𝜒𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm3.2an3  1118  necon4bddc  2317  necon4abiddc  2319  necon4bbiddc  2320  necon4biddc  2321
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