Theorem funcnvs1

Description: The converse of a singleton word is a function. (Contributed by AV, 22-Jan-2021)

	Ref	Expression
Assertion	funcnvs1	|- Fun `' <" A ">

Proof

Step	Hyp	Ref	Expression
1		funcnvsn	|- Fun `' { <. 0 , ( _I ` A ) >. }
2		df-s1	|- <" A "> = { <. 0 , ( _I ` A ) >. }
3	2	cnveqi	|- `' <" A "> = `' { <. 0 , ( _I ` A ) >. }
4	3	funeqi	|- ( Fun `' <" A "> <-> Fun `' { <. 0 , ( _I ` A ) >. } )
5	1 4	mpbir	|- Fun `' <" A ">