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Theorem syl3an2 1216
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an2.1
syl3an2.2
Assertion
Ref Expression
syl3an2

Proof of Theorem syl3an2
StepHypRef Expression
1 syl3an2.1 . . 3
2 syl3an2.2 . . . 4
323exp 1150 . . 3
41, 3syl5 28 . 2
543imp 1145 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by:  syl3an2b  1219  syl3an2br  1222  syl3anl2  1231
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