Theorem frege100

Description: One direction of dffrege99 . Proposition 100 of Frege1879 p. 72. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege99.z	|- Z e. U
Assertion	frege100	|- ( X ( ( t+ ` R ) u. _I ) Z -> ( -. X ( t+ ` R ) Z -> Z = X ) )

Proof

Step	Hyp	Ref	Expression
1		frege99.z	|- Z e. U
2	1	dffrege99	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) <-> X ( ( t+ ` R ) u. _I ) Z )
3		frege57aid	|- ( ( ( -. X ( t+ ` R ) Z -> Z = X ) <-> X ( ( t+ ` R ) u. _I ) Z ) -> ( X ( ( t+ ` R ) u. _I ) Z -> ( -. X ( t+ ` R ) Z -> Z = X ) ) )
4	2 3	ax-mp	|- ( X ( ( t+ ` R ) u. _I ) Z -> ( -. X ( t+ ` R ) Z -> Z = X ) )