Theorem rp-8frege 38098

Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-8frege	|- ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) )

Proof of Theorem rp-8frege

Step	Hyp	Ref	Expression
1		rp-6frege 38097	. 2 |- ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )
2		ax-frege2 38085	. 2 |- ( ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) ) -> ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ( ( ch -> ps ) -> th ) ) ) -> ( ph -> ( ps -> th ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085

This theorem is referenced by:  axfrege8  38101