Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
fndmu
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fnbr
Metamath Proof Explorer
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Unicode
Theorem
fndmu
Description:
A function has a unique domain.
(Contributed by
NM
, 11-Aug-1994)
Ref
Expression
Assertion
fndmu
⊢
F
Fn
A
∧
F
Fn
B
→
A
=
B
Proof
Step
Hyp
Ref
Expression
1
fndm
⊢
F
Fn
A
→
dom
⁡
F
=
A
2
fndm
⊢
F
Fn
B
→
dom
⁡
F
=
B
3
1
2
sylan9req
⊢
F
Fn
A
∧
F
Fn
B
→
A
=
B