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Theorem syl2an3an 1230
Description: syl3an 1212 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)
Hypotheses
Ref Expression
syl2an3an.1  |-  ( ph  ->  ps )
syl2an3an.2  |-  ( ph  ->  ch )
syl2an3an.3  |-  ( th 
->  ta )
syl2an3an.4  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
syl2an3an  |-  ( (
ph  /\  th )  ->  et )

Proof of Theorem syl2an3an
StepHypRef Expression
1 syl2an3an.1 . . 3  |-  ( ph  ->  ps )
2 syl2an3an.2 . . 3  |-  ( ph  ->  ch )
3 syl2an3an.3 . . 3  |-  ( th 
->  ta )
4 syl2an3an.4 . . 3  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
51, 2, 3, 4syl3an 1212 . 2  |-  ( (
ph  /\  ph  /\  th )  ->  et )
653anidm12 1227 1  |-  ( (
ph  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  cncongr1  10865
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