Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
fndm
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fndmi
Metamath Proof Explorer
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Theorem
fndm
Description:
The domain of a function.
(Contributed by
NM
, 2-Aug-1994)
Ref
Expression
Assertion
fndm
⊢
F
Fn
A
→
dom
⁡
F
=
A
Proof
Step
Hyp
Ref
Expression
1
df-fn
⊢
F
Fn
A
↔
Fun
⁡
F
∧
dom
⁡
F
=
A
2
1
simprbi
⊢
F
Fn
A
→
dom
⁡
F
=
A