ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant3r3 Unicode version

Theorem 3adant3r3 1216
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
Hypothesis
Ref Expression
3exp.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant3r3  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  th )

Proof of Theorem 3adant3r3
StepHypRef Expression
1 3exp.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1206 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
323adantr3 1160 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  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:  grpaddsubass  13049  grpsubsub4  13052  grpnpncan  13054  imasgrp2  13067  imasgrp  13068  cmn12  13262  abladdsub  13271  imasrng  13327  imasring  13431  opprrng  13444  opprring  13446  dvrass  13506  lss1  13695  mettri2  14339  xmetrtri  14353
  Copyright terms: Public domain W3C validator