Theorem iotacl

Description: Membership law for descriptions.

This can be useful for expanding an unbounded iota-based definition (see df-iota ). If you have a bounded iota-based definition, riotacl2 may be useful.

(Contributed by Andrew Salmon, 1-Aug-2011)

	Ref	Expression
Assertion	iotacl	|- ( E! x ph -> ( iota x ph ) e. { x | ph } )

Proof

Step	Hyp	Ref	Expression
1		iota4	|- ( E! x ph -> [. ( iota x ph ) / x ]. ph )
2		df-sbc	|- ( [. ( iota x ph ) / x ]. ph <-> ( iota x ph ) e. { x | ph } )
3	1 2	sylib	|- ( E! x ph -> ( iota x ph ) e. { x | ph } )