Theorem 2aryfvalel

Description: A binary (endo)function on a set X . (Contributed by AV, 20-May-2024)

	Ref	Expression
Assertion	2aryfvalel	Could not format assertion : No typesetting found for |- ( X e. V -> ( F e. ( 2 -aryF X ) <-> F : ( X ^m { 0 , 1 } ) --> X ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		2nn0	$$⊢2\in {\mathbb{N}}_0$$
2		fzo0to2pr	$$⊢\left(0..^2\right)=\left\{0,1\right\}$$
3	2	eqcomi	$$⊢\left\{0,1\right\}=\left(0..^2\right)$$
4	3	naryfvalel	Could not format ( ( 2 e. NN0 /\ X e. V ) -> ( F e. ( 2 -aryF X ) <-> F : ( X ^m { 0 , 1 } ) --> X ) ) : No typesetting found for |- ( ( 2 e. NN0 /\ X e. V ) -> ( F e. ( 2 -aryF X ) <-> F : ( X ^m { 0 , 1 } ) --> X ) ) with typecode |-
5	1 4	mpan	Could not format ( X e. V -> ( F e. ( 2 -aryF X ) <-> F : ( X ^m { 0 , 1 } ) --> X ) ) : No typesetting found for |- ( X e. V -> ( F e. ( 2 -aryF X ) <-> F : ( X ^m { 0 , 1 } ) --> X ) ) with typecode |-