Theorem dffrege69

Description: If from the proposition that x has property A it can be inferred generally, whatever x may be, that every result of an application of the procedure R to x has property A , then we say " Property A is hereditary in the R -sequence. Definition 69 of Frege1879 p. 55. (Contributed by RP, 28-Mar-2020)

	Ref	Expression
Assertion	dffrege69	|- ( A. x ( x e. A -> A. y ( x R y -> y e. A ) ) <-> R hereditary A )

Proof

Step	Hyp	Ref	Expression
1		dfhe3	|- ( R hereditary A <-> A. x ( x e. A -> A. y ( x R y -> y e. A ) ) )
2	1	bicomi	|- ( A. x ( x e. A -> A. y ( x R y -> y e. A ) ) <-> R hereditary A )