Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
funcnv0
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funcnvcnv
Metamath Proof Explorer
Ascii
Structured
Theorem
funcnv0
Description:
The converse of the empty set is a function.
(Contributed by
AV
, 7-Jan-2021)
Ref
Expression
Assertion
funcnv0
⊢
Fun
◡
∅
Proof
Step
Hyp
Ref
Expression
1
fun0
⊢
Fun ∅
2
cnv0
⊢
◡
∅ = ∅
3
2
funeqi
⊢
( Fun
◡
∅ ↔ Fun ∅ )
4
1
3
mpbir
⊢
Fun
◡
∅