Theorem frege106

Description: Whatever follows X in the R -sequence belongs to the R -sequence beginning with X . Proposition 106 of Frege1879 p. 73. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege103.z	|- Z e. V
Assertion	frege106	|- ( X ( t+ ` R ) Z -> X ( ( t+ ` R ) u. _I ) Z )

Proof

Step	Hyp	Ref	Expression
1		frege103.z	|- Z e. V
2	1	frege105	|- ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z )
3		frege37	|- ( ( ( -. X ( t+ ` R ) Z -> Z = X ) -> X ( ( t+ ` R ) u. _I ) Z ) -> ( X ( t+ ` R ) Z -> X ( ( t+ ` R ) u. _I ) Z ) )
4	2 3	ax-mp	|- ( X ( t+ ` R ) Z -> X ( ( t+ ` R ) u. _I ) Z )