Theorem frege96

Description: Every result of an application of the procedure R to an object that follows X in the R -sequence follows X in the R -sequence. Proposition 96 of Frege1879 p. 71. (Contributed by RP, 2-Jul-2020) (Revised by RP, 7-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	frege95.x	|- X e. U
	frege95.y	|- Y e. V
	frege95.z	|- Z e. W
	frege95.r	|- R e. A
Assertion	frege96	|- ( X ( t+ ` R ) Y -> ( Y R Z -> X ( t+ ` R ) Z ) )

Proof

Step	Hyp	Ref	Expression
1		frege95.x	|- X e. U
2		frege95.y	|- Y e. V
3		frege95.z	|- Z e. W
4		frege95.r	|- R e. A
5	1 2 3 4	frege95	|- ( Y R Z -> ( X ( t+ ` R ) Y -> X ( t+ ` R ) Z ) )
6		ax-frege8	|- ( ( Y R Z -> ( X ( t+ ` R ) Y -> X ( t+ ` R ) Z ) ) -> ( X ( t+ ` R ) Y -> ( Y R Z -> X ( t+ ` R ) Z ) ) )
7	5 6	ax-mp	|- ( X ( t+ ` R ) Y -> ( Y R Z -> X ( t+ ` R ) Z ) )