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Theorem bj-nnclav 34463
Description: When is substituted for 𝜓, this formula is the Clavius law with a doubly negated consequent, which is therefore a minimalistic tautology. Notice the non-intuitionistic proof from peirce 205 and pm2.27 42 chained using syl 17. (Contributed by BJ, 4-Dec-2023.)
Assertion
Ref Expression
bj-nnclav (((𝜑𝜓) → 𝜑) → ((𝜑𝜓) → 𝜓))

Proof of Theorem bj-nnclav
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21a2i 14 1 (((𝜑𝜓) → 𝜑) → ((𝜑𝜓) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  bj-nnclavi  34464  bj-nnclavc  34465  bj-peircestab  34470
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