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

Theorem sylnib 634
Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnib.1  |-  ( ph  ->  -.  ps )
sylnib.2  |-  ( ps  <->  ch )
Assertion
Ref Expression
sylnib  |-  ( ph  ->  -.  ch )

Proof of Theorem sylnib
StepHypRef Expression
1 sylnib.1 . 2  |-  ( ph  ->  -.  ps )
2 sylnib.2 . . 3  |-  ( ps  <->  ch )
32a1i 9 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
41, 3mtbid 630 1  |-  ( ph  ->  -.  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  sylnibr  635  inssdif0im  3327  undifexmid  3984  ordtriexmidlem2  4292  dmsn0el  4840  fidifsnen  6426  ltpopr  6899  caucvgprprlemnbj  6997  xrlttri3  9000  fzneuz  9246
  Copyright terms: Public domain W3C validator