Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
funrel
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0nelfun
Metamath Proof Explorer
Ascii
Structured
Theorem
funrel
Description:
A function is a relation.
(Contributed by
NM
, 1-Aug-1994)
Ref
Expression
Assertion
funrel
⊢
( Fun
𝐴
→ Rel
𝐴
)
Proof
Step
Hyp
Ref
Expression
1
df-fun
⊢
( Fun
𝐴
↔ ( Rel
𝐴
∧ (
𝐴
∘
◡
𝐴
) ⊆ I ) )
2
1
simplbi
⊢
( Fun
𝐴
→ Rel
𝐴
)