Theorem rp-7frege

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

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

Proof

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