Metamath Proof Explorer

Theorem frege63b

Description: Lemma for frege91 . Proposition 63 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	frege63b	\|- ( [ y / x ] ph -> ( ps -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) )

Step	Hyp	Ref	Expression
1		frege62b	\|- ( [ y / x ] ph -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) )
2		frege24	\|- ( ( [ y / x ] ph -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) -> ( [ y / x ] ph -> ( ps -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) ) )
3	1 2	ax-mp	\|- ( [ y / x ] ph -> ( ps -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) )

Step

Hyp

Ref

Expression

 |-  ( [ y / x ] ph -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) )

 |-  ( ( [ y / x ] ph -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) -> ( [ y / x ] ph -> ( ps -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) ) )

1 2

 |-  ( [ y / x ] ph -> ( ps -> ( A. x ( ph -> ch ) -> [ y / x ] ch ) ) )