Theorem impsingle-peirce

Description: Derivation of impsingle-peirce ( peirce ) from ax-mp and impsingle . It is step 28 in Lukasiewicz. (Contributed by Larry Lesyna and Jeffrey P. Machado, 2-Aug-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	impsingle-peirce	|- ( ( ( ph -> ps ) -> ph ) -> ph )

Proof

Step	Hyp	Ref	Expression
1		impsingle-step22	|- ( ph -> ph )
2		impsingle-step25	|- ( ( ph -> ph ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) )
3	1 2	ax-mp	|- ( ( ( ph -> ps ) -> ph ) -> ph )