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

Theorem mtbid 632
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.)
Hypotheses
Ref Expression
mtbid.min (𝜑 → ¬ 𝜓)
mtbid.maj (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
mtbid (𝜑 → ¬ 𝜒)

Proof of Theorem mtbid
StepHypRef Expression
1 mtbid.min . 2 (𝜑 → ¬ 𝜓)
2 mtbid.maj . . 3 (𝜑 → (𝜓𝜒))
32biimprd 156 . 2 (𝜑 → (𝜒𝜓))
41, 3mtod 624 1 (𝜑 → ¬ 𝜒)
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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  sylnib  636  eqneltrrd  2184  neleqtrd  2185  eueq3dc  2789  efrirr  4180  fidcenumlemrks  6662  nqnq0pi  6997  zdclt  8824  frec2uzf1od  9813  expnegap0  9963  ibcval5  10171  zfz1isolemiso  10244  iseqcoll  10247  fisumss  10784  rpdvds  11359  oddpwdclemodd  11428
  Copyright terms: Public domain W3C validator