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Theorem adantrlr 477
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
adantrlr  |-  ( (
ph  /\  ( ( ps  /\  ta )  /\  ch ) )  ->  th )

Proof of Theorem adantrlr
StepHypRef Expression
1 simpl 108 . 2  |-  ( ( ps  /\  ta )  ->  ps )
2 adantr2.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylanr1 402 1  |-  ( (
ph  /\  ( ( ps  /\  ta )  /\  ch ) )  ->  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:  genpdisj  7351  ltexprlemdisj  7434  addcanprlemu  7443  addsrmo  7571  mulsrmo  7572
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