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now the most important use of universal introduction as a rule is in conditional generalization this is where we say supposing that of some constant c selected arbitrarily if c is an f then c is a g well since this held for an arbitrarily selected object we can generalize and say all fs are gs that is everything is such that if its an f then its g lets see how this works now most universal claims dont take the form of unconditional universal predications of the form axpx that is to say everything is a p there are certain predicates that work with this like for instance everything is an object or everything is a thing but these arent really that interesting what we want to be able to do is to make proofs of conditional statements of the form every f is a g and we do this by making use of our arbitrary names again so suppose that we want to prove that all fs are gs we assume that e e in these examples has been just our arbitrary constant we assume that e is an f we derive in the
