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Theorem 3adantl3 1124
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
3adantl3  |-  ( ( ( ph  /\  ps  /\ 
ta )  /\  ch )  ->  th )

Proof of Theorem 3adantl3
StepHypRef Expression
1 3simpa 963 . 2  |-  ( (
ph  /\  ps  /\  ta )  ->  ( ph  /\  ps ) )
2 3adantl.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylan 281 1  |-  ( ( ( ph  /\  ps  /\ 
ta )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
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 depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  ltsopr  7372  lediv2a  8617  muldvds1  11430  muldvds2  11431  dvdscmul  11432  dvdsmulc  11433  rpexp  11743  iscnp4  12298  cnpnei  12299  xblm  12497
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