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Theorem 3adant3r1 1214
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
Hypothesis
Ref Expression
3exp.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant3r1  |-  ( (
ph  /\  ( ta  /\ 
ps  /\  ch )
)  ->  th )

Proof of Theorem 3adant3r1
StepHypRef Expression
1 3exp.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1206 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
323adantr1 1158 1  |-  ( (
ph  /\  ( ta  /\ 
ps  /\  ch )
)  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  grpsubsub  12999  grpnnncan2  13007  imasgrp2  13018  mulgnn0ass  13064  mulgsubdir  13068  cmn32  13204  ablsubadd  13212  imasrng  13271  imasring  13375  opprrng  13388  opprring  13390  xmettri3  14271  mettri3  14272  xmetrtri  14273  rprelogbmulexp  14771
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