Universally
UNIVERS'ALLY, adverb With extension to the whole; in a manner to comprehend all; without exception. Air is a fluid universally diffused. God's laws are universally binding on his creatures.
[Note - Universal and its derivatives are used in common discourse for general. This kind of universality is by the schoolmen called moral, as admitting of some exceptions, in distinction from metophysical, which precludes all exceptions.]