Theorem frege119

Description: Lemma for frege120 . Proposition 119 of Frege1879 p. 78. (Contributed by RP, 8-Jul-2020) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	frege116.x	|- X e. U
	frege118.y	|- Y e. V
Assertion	frege119	|- ( ( A. a ( Y R a -> a = X ) -> ( Y R A -> A = X ) ) -> ( Fun `' `' R -> ( Y R X -> ( Y R A -> A = X ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege116.x	|- X e. U
2		frege118.y	|- Y e. V
3	1 2	frege118	|- ( Fun `' `' R -> ( Y R X -> A. a ( Y R a -> a = X ) ) )
4		frege19	|- ( ( Fun `' `' R -> ( Y R X -> A. a ( Y R a -> a = X ) ) ) -> ( ( A. a ( Y R a -> a = X ) -> ( Y R A -> A = X ) ) -> ( Fun `' `' R -> ( Y R X -> ( Y R A -> A = X ) ) ) ) )
5	3 4	ax-mp	|- ( ( A. a ( Y R a -> a = X ) -> ( Y R A -> A = X ) ) -> ( Fun `' `' R -> ( Y R X -> ( Y R A -> A = X ) ) ) )