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Theorem syl2an2 559
Description: syl2an 283 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
syl2an2.1  |-  ( ph  ->  ps )
syl2an2.2  |-  ( ( ch  /\  ph )  ->  th )
syl2an2.3  |-  ( ( ps  /\  th )  ->  ta )
Assertion
Ref Expression
syl2an2  |-  ( ( ch  /\  ph )  ->  ta )

Proof of Theorem syl2an2
StepHypRef Expression
1 syl2an2.1 . . 3  |-  ( ph  ->  ps )
2 syl2an2.2 . . 3  |-  ( ( ch  /\  ph )  ->  th )
3 syl2an2.3 . . 3  |-  ( ( ps  /\  th )  ->  ta )
41, 2, 3syl2an 283 . 2  |-  ( (
ph  /\  ( ch  /\ 
ph ) )  ->  ta )
54anabss7 548 1  |-  ( ( ch  /\  ph )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
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
This theorem is referenced by:  qbtwnz  9390  fihashf1rn  9865  isumrblem  10400  divalgmod  10534  gcdsupex  10556  gcdsupcl  10557  cncongr2  10693  isprm3  10707
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