Theorem frege66c

Description: Swap antecedents of frege65c . Proposition 66 of Frege1879 p. 54. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	frege59c.a	|- A e. B
Assertion	frege66c	|- ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [. A / x ]. ch -> [. A / x ]. ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege59c.a	|- A e. B
2	1	frege65c	|- ( A. x ( ch -> ph ) -> ( A. x ( ph -> ps ) -> ( [. A / x ]. ch -> [. A / x ]. ps ) ) )
3		ax-frege8	|- ( ( A. x ( ch -> ph ) -> ( A. x ( ph -> ps ) -> ( [. A / x ]. ch -> [. A / x ]. ps ) ) ) -> ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [. A / x ]. ch -> [. A / x ]. ps ) ) ) )
4	2 3	ax-mp	|- ( A. x ( ph -> ps ) -> ( A. x ( ch -> ph ) -> ( [. A / x ]. ch -> [. A / x ]. ps ) ) )