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

Proof of Theorem adantrrl
StepHypRef Expression
1 simpr 447 . 2  |-  ( ( ta  /\  ch )  ->  ch )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr2 634 1  |-  ( (
ph  /\  ( ps  /\  ( ta  /\  ch ) ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  1stconst  6207  zorn2lem6  8128  ltmul12a  9612  neiint  16841  neissex  16864  1stcfb  17171  1stcrest  17179  grporcan  20888  mdslmd3i  22912  colineardim1  24684  cvratlem  29610  ps-2  29667
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 177  df-an 360
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