Theorem frege112

Description: Identity implies belonging to the R -sequence beginning with self. Proposition 112 of Frege1879 p. 76. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege112.z	|- Z e. V
Assertion	frege112	|- ( Z = X -> X ( ( t+ ` R ) u. _I ) Z )

Proof

Step	Hyp	Ref	Expression
1		frege112.z	|- Z e. V
2	1	frege105	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z )
3		frege11	|- ( ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z ) -> ( Z = X -> X ( ( t+ ` R ) u. _I ) Z ) )
4	2 3	ax-mp	|- ( Z = X -> X ( ( t+ ` R ) u. _I ) Z )