Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
fnrel
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fndm
Metamath Proof Explorer
Ascii
Structured
Theorem
fnrel
Description:
A function with domain is a relation.
(Contributed by
NM
, 1-Aug-1994)
Ref
Expression
Assertion
fnrel
⊢
(
𝐹
Fn
𝐴
→ Rel
𝐹
)
Proof
Step
Hyp
Ref
Expression
1
fnfun
⊢
(
𝐹
Fn
𝐴
→ Fun
𝐹
)
2
funrel
⊢
( Fun
𝐹
→ Rel
𝐹
)
3
1
2
syl
⊢
(
𝐹
Fn
𝐴
→ Rel
𝐹
)