Theorem 1aryfvalel

Description: A unary (endo)function on a set X . (Contributed by AV, 15-May-2024)

	Ref	Expression
Assertion	1aryfvalel	Could not format assertion : No typesetting found for |- ( X e. V -> ( F e. ( 1 -aryF X ) <-> F : ( X ^m { 0 } ) --> X ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		1nn0	$$⊢1\in {\mathbb{N}}_0$$
2		fzo01	$$⊢\left(0..^1\right)=\left\{0\right\}$$
3	2	eqcomi	$$⊢\left\{0\right\}=\left(0..^1\right)$$
4	3	naryfvalel	Could not format ( ( 1 e. NN0 /\ X e. V ) -> ( F e. ( 1 -aryF X ) <-> F : ( X ^m { 0 } ) --> X ) ) : No typesetting found for |- ( ( 1 e. NN0 /\ X e. V ) -> ( F e. ( 1 -aryF X ) <-> F : ( X ^m { 0 } ) --> X ) ) with typecode |-
5	1 4	mpan	Could not format ( X e. V -> ( F e. ( 1 -aryF X ) <-> F : ( X ^m { 0 } ) --> X ) ) : No typesetting found for |- ( X e. V -> ( F e. ( 1 -aryF X ) <-> F : ( X ^m { 0 } ) --> X ) ) with typecode |-