enter image description hereDefinition 2.5 Let Γ be a set of wfs. of L (which may or may not be axioms or theorems of L). A sequence Al,..., An, of wfs. of L is a deduction from Γ if for each i (1 -< i -< n), one of the following holds:
(a) Ai is an axiom of L,
(b) Ai is a member of Γ, or
(c) Ai follows from two previous members of the sequence as a direct consequence using MP. So a deduction from Γ is just a 'proof' in which the members of Γ are considered as temporary axioms. The last member, An, of a sequence which is a deduction from Γ is said to be deducible from Γ or to be a consequence of Γ in L.
Above is the original text. My question comes from the sentence of (a) : Since Ai is an axiom, how did it deduce from Γ, considering that Γ might not be the axiom set?