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Theorem adantrlr 722
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 457 . 2  |-  ( ( ps  /\  ta )  ->  ps )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr1 652 1  |-  ( (
ph  /\  ( ( ps  /\  ta )  /\  ch ) )  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  smoord  6939  lediv12a  10339  nrmmetd  20302  pntrmax  22949  ablo4  23946  mdslmd3i  25908  atom1d  25929  fdc  28809  incsequz  28812  crngm4  28971  ps-2  33480
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