Metamath Proof Explorer


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 x x A y x R y y A R hereditary A

Proof

Step Hyp Ref Expression
1 dfhe3 R hereditary A x x A y x R y y A
2 1 bicomi x x A y x R y y A R hereditary A