Theorem rp-7frege 38095

Description: Distribute antecedent and add another. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-7frege	|- ( ( ph -> ( ps -> ch ) ) -> ( th -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) )

Proof of Theorem rp-7frege

Step	Hyp	Ref	Expression
1		ax-frege2 38085	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2		rp-frege24 38091	. 2 |- ( ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( th -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ch ) ) -> ( th -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) )

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