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Theorem syl3an2cOLDOLD 26438
 Description: A syllogism inference combined with contraction. (Moved to syl13anc 1184 in main set.mm and may be deleted by mathbox owner, JM. --NM 8-Sep-2011.) (Contributed by Jeff Madsen, 17-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
syl3an2cOLD.1
syl3an2cOLD.2
syl3an2cOLD.3
syl3an2cOLD.4
syl3an2cOLD.5
Assertion
Ref Expression
syl3an2cOLDOLD

Proof of Theorem syl3an2cOLDOLD
StepHypRef Expression
1 syl3an2cOLD.2 . 2
2 syl3an2cOLD.3 . 2
3 syl3an2cOLD.4 . 2
4 syl3an2cOLD.5 . 2
5 syl3an2cOLD.1 . 2
61, 2, 3, 4, 5syl13anc 1184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   w3a 934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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