Metamath Proof Explorer


Theorem pm2.18OLD

Description: Obsolete version of pm2.18 as of 17-Nov-2023. (Contributed by NM, 29-Dec-1992) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion pm2.18OLD
|- ( ( -. ph -> ph ) -> ph )

Proof

Step Hyp Ref Expression
1 pm2.21
 |-  ( -. ph -> ( ph -> -. ( -. ph -> ph ) ) )
2 1 a2i
 |-  ( ( -. ph -> ph ) -> ( -. ph -> -. ( -. ph -> ph ) ) )
3 2 con4d
 |-  ( ( -. ph -> ph ) -> ( ( -. ph -> ph ) -> ph ) )
4 3 pm2.43i
 |-  ( ( -. ph -> ph ) -> ph )