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Theorem adantrrr 471
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 107 . 2  |-  ( ( ch  /\  ta )  ->  ch )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr2 397 1  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  ta ) ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  2ndconst  5874  genpdisj  6775  ltexprlemdisj  6858  addsrmo  6982  mulsrmo  6983  lemul12b  8006
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