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Theorem adantrll 702
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
adantrll  |-  ( (
ph  /\  ( ( ta  /\  ps )  /\  ch ) )  ->  th )

Proof of Theorem adantrll
StepHypRef Expression
1 simpr 447 . 2  |-  ( ( ta  /\  ps )  ->  ps )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr1 633 1  |-  ( (
ph  /\  ( ( ta  /\  ps )  /\  ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  lo1le  12125  nrmmetd  18097  mdslmd3i  22912
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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