PROVE_HYP : thm -> thm -> thm
When applied to two theorems, PROVE_HYP returns a theorem having the conclusion of the second. The new hypotheses are the union of the two hypothesis sets (first deleting, however, the conclusion of the first theorem from the hypotheses of the second).
A1 |- t1 A2 |- t2
------------------------ PROVE_HYP
A1 u (A2 - {t1}) |- t2