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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  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
syl3an2cOLD.2  |-  ( et 
->  ph )
syl3an2cOLD.3  |-  ( et 
->  ps )
syl3an2cOLD.4  |-  ( et 
->  ch )
syl3an2cOLD.5  |-  ( et 
->  th )
Assertion
Ref Expression
syl3an2cOLDOLD  |-  ( et 
->  ta )

Proof of Theorem syl3an2cOLDOLD
StepHypRef Expression
1 syl3an2cOLD.2 . 2  |-  ( et 
->  ph )
2 syl3an2cOLD.3 . 2  |-  ( et 
->  ps )
3 syl3an2cOLD.4 . 2  |-  ( et 
->  ch )
4 syl3an2cOLD.5 . 2  |-  ( et 
->  th )
5 syl3an2cOLD.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
61, 2, 3, 4, 5syl13anc 1184 1  |-  ( et 
->  ta )
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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