ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  con2d Unicode version

Theorem con2d 624
Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993.) (Revised by NM, 12-Feb-2013.)
Hypothesis
Ref Expression
con2d.1  |-  ( ph  ->  ( ps  ->  -.  ch ) )
Assertion
Ref Expression
con2d  |-  ( ph  ->  ( ch  ->  -.  ps ) )

Proof of Theorem con2d
StepHypRef Expression
1 con2d.1 . . . 4  |-  ( ph  ->  ( ps  ->  -.  ch ) )
2 ax-in2 615 . . . 4  |-  ( -. 
ch  ->  ( ch  ->  -. 
ps ) )
31, 2syl6 33 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  -.  ps )
) )
43com23 78 . 2  |-  ( ph  ->  ( ch  ->  ( ps  ->  -.  ps )
) )
5 pm2.01 616 . 2  |-  ( ( ps  ->  -.  ps )  ->  -.  ps )
64, 5syl6 33 1  |-  ( ph  ->  ( ch  ->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 614  ax-in2 615
This theorem is referenced by:  mt2d  625  con3d  631  pm3.2im  637  con2  643  pm2.65  659  con1biimdc  873  exists2  2123  necon2ad  2404  necon2bd  2405  minel  3484  nlimsucg  4561  poirr2  5016  funun  5255  imadif  5291  infnlbti  7018  mkvprop  7149  addnidpig  7313  zltnle  9275  zdcle  9305  btwnnz  9323  prime  9328  icc0r  9900  fznlem  10014  qltnle  10219  bcval4  10703  seq3coll  10793  fsum3cvg  11357  fsumsplit  11386  fproddccvg  11551  fprodsplitdc  11575  2sqpwodd  12146  pockthg  12325  prmunb  12330  logbgcd1irr  14018  lgsne0  14072
  Copyright terms: Public domain W3C validator