IMP_TRANS

Drule.IMP_TRANS : (thm -> thm -> thm)

Implements the transitivity of implication.

When applied to theorems A1 |- t1 ==> t2 and A2 |- t2 ==> t3, the inference rule IMP_TRANS returns the theorem A1 u A2 |- t1 ==> t3.

    A1 |- t1 ==> t2   A2 |- t2 ==> t3
   -----------------------------------  IMP_TRANS
         A1 u A2 |- t1 ==> t3

Failure

Fails unless the theorems are both implicative, with the consequent of the first being the same as the antecedent of the second (up to alpha-conversion).

See also

Drule.IMP_ANTISYM_RULE, Thm.SYM, Thm.TRANS