Theorem frege73

Description: Lemma for frege87 . Proposition 73 of Frege1879 p. 59. (Contributed by RP, 28-Mar-2020) (Revised by RP, 5-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	frege73.x	|- X e. U
	frege73.y	|- Y e. V
Assertion	frege73	|- ( ( R hereditary A -> X e. A ) -> ( R hereditary A -> ( X R Y -> Y e. A ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege73.x	|- X e. U
2		frege73.y	|- Y e. V
3	1 2	frege72	|- ( R hereditary A -> ( X e. A -> ( X R Y -> Y e. A ) ) )
4		ax-frege2	|- ( ( R hereditary A -> ( X e. A -> ( X R Y -> Y e. A ) ) ) -> ( ( R hereditary A -> X e. A ) -> ( R hereditary A -> ( X R Y -> Y e. A ) ) ) )
5	3 4	ax-mp	|- ( ( R hereditary A -> X e. A ) -> ( R hereditary A -> ( X R Y -> Y e. A ) ) )