In mathematical textbooks (for instance the Kelly's General Topology or the Spivak's Calculus) a theorem has hypotheses and a thesis.
In formal mathematics is different: A theorem of a formal theory L is a wff φ of L such that φ is the last wff of some proof in L. Such a proof is called a proof of φ in L.
However, in in formal mathematics there is something like hypotheses found in textbooks:
A wff φ is said to be a consequence, in a formal theory L, of a finite set $\Gamma$ of wffs if and only if there is a sequence $\beta_1,...,\beta_k$ of wffs such that φ is $\beta_k$ and, for each …
In formal mathematics is different: A theorem of a formal theory L is a wff φ of L such that φ is the last wff of some proof in L. Such a proof is called a proof of φ in L.
However, in in formal mathematics there is something like hypotheses found in textbooks:
A wff φ is said to be a consequence, in a formal theory L, of a finite set $\Gamma$ of wffs if and only if there is a sequence $\beta_1,...,\beta_k$ of wffs such that φ is $\beta_k$ and, for each …
