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wikipedia says "An inference rule containing no premises is called an axiom schema or it if contains no metavariables simply an axiom."

but why can't we trivially make a premise ("A is true") part of an axiom schema ("B -> C") by doing something like "A & B -> C"?

  1. what's the difference? (my background is some ugrad math)
  2. what's a concrete difference in what they can do?

thank you

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    $\begingroup$ This is not a research level question. A more careful reading of the Wikipedia article should clear up your first question entirely and help you understand the second. You could also look at the references in the Wikipedia article. $\endgroup$
    – Colin McLarty
    Commented Jan 20, 2013 at 16:33
  • $\begingroup$ oh, sorry about that. i read the faq now. $\endgroup$
    – sboosali
    Commented Jan 21, 2013 at 18:25

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