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Theorem syl2an3an 1287
Description: syl3an 1269 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 1269 . 2  |-  ( (
ph  /\  ph  /\  th )  ->  et )
653anidm12 1284 1  |-  ( (
ph  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 967
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 969
This theorem is referenced by:  expcnvap0  11437  efexp  11617  cncongr1  12029  uptx  12872  logbgcd1irr  13483
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