Theorem adh-jarrsc

Description: Replacement of a nested antecedent with an outer antecedent. Commuted simplificated form of elimination of a nested antecedent. Also holds intuitionistically. Polish prefix notation: CCCpqrCsCqr . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.)

	Ref	Expression
Assertion	adh-jarrsc	|- ( ( ( ph -> ps ) -> ch ) -> ( th -> ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		jarr	|- ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) )
2		ax-1	|- ( ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) ) -> ( th -> ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) ) ) )
3	1 2	ax-mp	|- ( th -> ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) ) )
4		pm2.04	|- ( ( th -> ( ( ( ph -> ps ) -> ch ) -> ( ps -> ch ) ) ) -> ( ( ( ph -> ps ) -> ch ) -> ( th -> ( ps -> ch ) ) ) )
5	3 4	ax-mp	|- ( ( ( ph -> ps ) -> ch ) -> ( th -> ( ps -> ch ) ) )