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Theorem adantrrr 478
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
adantrrr  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  ta ) ) )  ->  th )

Proof of Theorem adantrrr
StepHypRef Expression
1 simpl 108 . 2  |-  ( ( ch  /\  ta )  ->  ch )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr2 402 1  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  ta ) ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  2ndconst  6119  genpdisj  7331  ltexprlemdisj  7414  addsrmo  7551  mulsrmo  7552  axpre-suploclemres  7709  lemul12b  8619  tgcl  12233  neissex  12334
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