Theorem reuaiotaiota

Description: The iota and the alternate iota over a wff ph are equal iff there is a unique value x satisfying ph . (Contributed by AV, 25-Aug-2022)

	Ref	Expression
Assertion	reuaiotaiota	|- ( E! x ph <-> ( iota x ph ) = ( iota' x ph ) )

Proof

Step	Hyp	Ref	Expression
1		euabsneu	|- ( E! x ph <-> E! y { x | ph } = { y } )
2		reuabaiotaiota	|- ( E! y { x | ph } = { y } <-> ( iota x ph ) = ( iota' x ph ) )
3	1 2	bitri	|- ( E! x ph <-> ( iota x ph ) = ( iota' x ph ) )