Theorem frege74

Description: If X has a property A that is hereditary in the R -sequence, then every result of a application of the procedure R to X has the property A . Proposition 74 of Frege1879 p. 60. (Contributed by RP, 28-Mar-2020) (Revised by RP, 5-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	frege74.x	|- X e. U
	frege74.y	|- Y e. V
Assertion	frege74	|- ( X e. A -> ( R hereditary A -> ( X R Y -> Y e. A ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege74.x	|- X e. U
2		frege74.y	|- Y e. V
3	1 2	frege72	|- ( R hereditary A -> ( X e. A -> ( X R Y -> Y e. A ) ) )
4		ax-frege8	|- ( ( R hereditary A -> ( X e. A -> ( X R Y -> Y e. A ) ) ) -> ( X e. A -> ( R hereditary A -> ( X R Y -> Y e. A ) ) ) )
5	3 4	ax-mp	|- ( X e. A -> ( R hereditary A -> ( X R Y -> Y e. A ) ) )