Theorem impsingle-peirce 1647

Description: Derivation of impsingle-peirce (peirce 205) from ax-mp 5 and impsingle 1635. 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.)

Assertion

Ref	Expression
impsingle-peirce	⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)

Proof of Theorem impsingle-peirce

Step	Hyp	Ref	Expression
1		impsingle-step22 1644	. 2 ⊢ (𝜑 → 𝜑)
2		impsingle-step25 1645	. 2 ⊢ ((𝜑 → 𝜑) → (((𝜑 → 𝜓) → 𝜑) → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)