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Theorem adantlrr 452
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
adantlrr  |-  ( ( ( ph  /\  ( ps  /\  ta ) )  /\  ch )  ->  th )

Proof of Theorem adantlrr
StepHypRef Expression
1 simpl 102 . 2  |-  ( ( ps  /\  ta )  ->  ps )
2 adantl2.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylanl2 383 1  |-  ( ( ( ph  /\  ( ps  /\  ta ) )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  distrlem1prl  6680  distrlem1pru  6681  cnegex  7189
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