The result of applying a deduction rule with more than one hypothesis is the set of deduction rules obtained by deleting its first hypothesis (i.e., the one that was matched) and applying the substitution(s) that matched this hypothesis to the remainder of the deduction rule.
(The result of applying a deduction rule with more than one hypothesis; is; the set of deduction rules) (the substitution; matched; ) (deduction rules; obtained; ) (deduction rules; by deleting; its first hypothesis) (i.e., the one; was matched; )
The result of applying a deduction rule with more than one hypothesis the substitution deduction rules deduction rules i.e., the one
is matched obtained by deleting was matched
the set of deduction rules
its first hypothesis