Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nnclavc Structured version   Visualization version   GIF version

Theorem bj-nnclavc 34465
Description: Commuted form of bj-nnclav 34463. Notice the non-intuitionistic proof from bj-peircei 34483 and imim1i 63. (Contributed by BJ, 30-Jul-2024.) A proof which is shorter when compressed uses embantd 59. (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nnclavc ((𝜑𝜓) → (((𝜑𝜓) → 𝜑) → 𝜓))

Proof of Theorem bj-nnclavc
StepHypRef Expression
1 bj-nnclav 34463 . 2 (((𝜑𝜓) → 𝜑) → ((𝜑𝜓) → 𝜓))
21com12 32 1 ((𝜑𝜓) → (((𝜑𝜓) → 𝜑) → 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-nnclavci  34466
  Copyright terms: Public domain W3C validator