Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
frn
Next ⟩
frnd
Metamath Proof Explorer
Ascii
Unicode
Theorem
frn
Description:
The range of a mapping.
(Contributed by
NM
, 3-Aug-1994)
Ref
Expression
Assertion
frn
⊢
F
:
A
⟶
B
→
ran
⁡
F
⊆
B
Proof
Step
Hyp
Ref
Expression
1
df-f
⊢
F
:
A
⟶
B
↔
F
Fn
A
∧
ran
⁡
F
⊆
B
2
1
simprbi
⊢
F
:
A
⟶
B
→
ran
⁡
F
⊆
B