IMPLIES

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English language form: if P, then Q

Symbolic abbreviation: P Q

Typical examples include:

  if P, Q

  P implies Q

  Q if P

  Q on condition that P

  P only if Q

  Q in case that P

  only if Q P

  Q provided that P

  P is sufficient for Q

  Q is necessary for P

  for Q it is sufficient that P

  for P it is necessary that Q

  Q given that P

  IF P, then Q