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Theorem adantrrl 723
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
adantrrl  |-  ( (
ph  /\  ( ps  /\  ( ta  /\  ch ) ) )  ->  th )

Proof of Theorem adantrrl
StepHypRef Expression
1 simpr 461 . 2  |-  ( ( ta  /\  ch )  ->  ch )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr2 653 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:  1stconst  6761  zorn2lem6  8771  ltmul12a  10286  mrcmndind  15596  neiint  18824  neissex  18847  1stcfb  19165  1stcrest  19173  grporcan  23843  mdslmd3i  25871  colineardim1  28226  cvratlem  33371  ps-2  33428
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