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Theorem syl3anb 1225
Description: A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)
Hypotheses
Ref Expression
syl3anb.1
syl3anb.2
syl3anb.3
syl3anb.4
Assertion
Ref Expression
syl3anb

Proof of Theorem syl3anb
StepHypRef Expression
1 syl3anb.1 . . 3
2 syl3anb.2 . . 3
3 syl3anb.3 . . 3
41, 2, 33anbi123i 1140 . 2
5 syl3anb.4 . 2
64, 5sylbi 187 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   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:  syl3anbr  1226
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