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Theorem adantrlr 704
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
adantrlr  |-  ( (
ph  /\  ( ( ps  /\  ta )  /\  ch ) )  ->  th )

Proof of Theorem adantrlr
StepHypRef Expression
1 simpl 444 . 2  |-  ( ( ps  /\  ta )  ->  ps )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr1 634 1  |-  ( (
ph  /\  ( ( ps  /\  ta )  /\  ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  smoord  6594  lediv12a  9867  nrmmetd  18583  pntrmax  21219  ablo4  21836  mdslmd3i  23796  atom1d  23817  fdc  26347  incsequz  26350  crngm4  26511  ps-2  29972
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 178  df-an 361
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