MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nic-swap Structured version   Visualization version   GIF version

Theorem nic-swap 1671
Description: The connector is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-swap ((𝜃𝜑) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))

Proof of Theorem nic-swap
StepHypRef Expression
1 nic-id 1670 . 2 (𝜑 ⊼ (𝜑𝜑))
2 nic-ax 1665 . 2 ((𝜑 ⊼ (𝜑𝜑)) ⊼ ((𝜏 ⊼ (𝜏𝜏)) ⊼ ((𝜃𝜑) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))))
31, 2nic-mp 1663 1 ((𝜃𝜑) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wnan 1475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208  df-an 397  df-nan 1476
This theorem is referenced by:  nic-isw1  1672  nic-isw2  1673  nic-bijust  1679  nic-luk1  1683
  Copyright terms: Public domain W3C validator