Unfortunately, I had no time to follow the whole discussion in detail, but
I think David's proposal is acceptable:
• deduction form: A kind of assertion with zero or more hypotheses
> where the conclusion is an implication with a wff variable as the
> antecedent (usually φ), and every hypothesis ($e statement) is either
> (1) an implication with the same antecedent as the conclusion, (2) a
> definition, or (3) a statement of not-freeness ` F/ ` . {... existing text
> ...}
>
Maybe further results of this discussion can be documented on page/section
http://us.metamath.org/mpeuni/mmnatded.html#special-cases. Can we insert
this link also into set.mm?
Alexander
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