Theorem impsingle-step21

Derivation of impsingle-step21 from [ax-mp] and impsingle. It is used as a lemma in the proof of imim1 from impsingle. It is Step 21 in Lukasiewicz, where it appears as 'CCCCprqqCCqrCpr' using parenthesis-free prefix notation. (Contributed by Larry Lesyna and Jeffrey P. Machado, 2-Aug-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Conclusion
\( \vdash (((\varphi \rightarrow \psi) \rightarrow \chi) \rightarrow \chi) \rightarrow (\chi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi \)
Proof
l0
impsingle-step15
\( \vdash ((\chi \rightarrow \varphi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi) \rightarrow (\chi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi \)
impsingle-step20
\( \vdash (((\chi \rightarrow \varphi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi) \rightarrow (\chi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi) \rightarrow (((\varphi \rightarrow \psi) \rightarrow \chi) \rightarrow \chi) \rightarrow (\chi \rightarrow \psi) \rightarrow \varphi \rightarrow \psi \)
ax-mp l0 _