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Theorem simp112 1085
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp112  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ps )

Proof of Theorem simp112
StepHypRef Expression
1 simp12 986 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ps )
213ad2ant1 976 1  |-  ( ( ( ( ph  /\  ps  /\  ch )  /\  th 
/\  ta )  /\  et  /\  ze )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  axcontlem4  24595  ps-2b  29671  llncvrlpln2  29746  4atlem11b  29797  4atlem12b  29800  2lnat  29973  cdlemblem  29982  4atexlemex6  30263  cdleme24  30541  cdleme26ee  30549  cdlemg2idN  30785  cdlemg31c  30888  cdlemk26-3  31095  dihglblem2N  31484
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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