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Theorem sylnib 676
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 672 1  |-  ( ph  ->  -.  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  sylnibr  677  neqcomd  2182  inssdif0im  3490  undifexmid  4193  ordtriexmidlem2  4519  dmsn0el  5098  fidifsnen  6869  ctssdccl  7109  nninfwlpoimlemginf  7173  onntri35  7235  onntri45  7239  2omotaplemap  7255  exmidapne  7258  ltpopr  7593  caucvgprprlemnbj  7691  xrlttri3  9795  fzneuz  10098  iseqf1olemqcl  10483  iseqf1olemnab  10485  iseqf1olemab  10486  exp3val  10519  pwle2  14630
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