Theorem frege105

Description: Proposition 105 of Frege1879 p. 73. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege103.z	|- Z e. V
Assertion	frege105	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z )

Proof

Step	Hyp	Ref	Expression
1		frege103.z	|- Z e. V
2	1	dffrege99	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) <-> X ( ( t+ ` R ) u. _I ) Z )
3		frege52aid	|- ( ( ( -. X ( t+ ` R ) Z -> Z = X ) <-> X ( ( t+ ` R ) u. _I ) Z ) -> ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z ) )
4	2 3	ax-mp	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z )