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Theorem syl2an2r 560
Description: syl2anr 284 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
syl2an2r.1  |-  ( ph  ->  ps )
syl2an2r.2  |-  ( (
ph  /\  ch )  ->  th )
syl2an2r.3  |-  ( ( ps  /\  th )  ->  ta )
Assertion
Ref Expression
syl2an2r  |-  ( (
ph  /\  ch )  ->  ta )

Proof of Theorem syl2an2r
StepHypRef Expression
1 syl2an2r.1 . . 3  |-  ( ph  ->  ps )
2 syl2an2r.2 . . 3  |-  ( (
ph  /\  ch )  ->  th )
3 syl2an2r.3 . . 3  |-  ( ( ps  /\  th )  ->  ta )
41, 2, 3syl2an 283 . 2  |-  ( (
ph  /\  ( ph  /\ 
ch ) )  ->  ta )
54anabss5 543 1  |-  ( (
ph  /\  ch )  ->  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:  op1stbg  4236  supelti  6474  supmaxti  6476  infminti  6499  frecuzrdgsuc  9496  sizeunlem  9828  serif0  10327  divalglemnqt  10464  lcmid  10606
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