"Univocal" is a word made of two parts. Both are derived from Latin. The prefix "uni" means "one" or "singular", and "vocal" refers to "voice". Thus the meaning of "univocal" is "of one voice", or "having one meaning".
It is not a word in common use -- so much so that my in-browser dictionary flags it as wrong. As Canadian Yankee mentions, unanimous is a much more common word that means the same thing (again from the Latin, uni="one" and animus="mind", "of one mind").
If you feel you must use it, then your sentence is fine as written. You can use univocal in the same way as you use unanimous:
The legislature passed the bill with univocal approval.
The union's support of the candidate was univocal.
One more warning: It's likely people will think you meant to write unequivocal (un="not", equi="equal", voc="voice", "not having two equal meanings") because, again, that is a much more common word. While the meaning is similar, it's used to indicate certainty rather than agreement.
The union's support of the candidate was unequivocal. (without debate)