Metamath Proof Explorer


Theorem bj-nnclav

Description: When F. is substituted for ps , this formula is the Clavius law with a doubly negated consequent, which is therefore a minimalistic tautology. Notice the non-intuitionistic proof from peirce and pm2.27 chained using syl . (Contributed by BJ, 4-Dec-2023)

Ref Expression
Assertion bj-nnclav
|- ( ( ( ph -> ps ) -> ph ) -> ( ( ph -> ps ) -> ps ) )

Proof

Step Hyp Ref Expression
1 id
 |-  ( ( ph -> ps ) -> ( ph -> ps ) )
2 1 a2i
 |-  ( ( ( ph -> ps ) -> ph ) -> ( ( ph -> ps ) -> ps ) )