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Theorem nic-swap 1752
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 1751 . 2 (𝜑 ⊼ (𝜑𝜑))
2 nic-ax 1746 . 2 ((𝜑 ⊼ (𝜑𝜑)) ⊼ ((𝜏 ⊼ (𝜏𝜏)) ⊼ ((𝜃𝜑) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))))
31, 2nic-mp 1744 1 ((𝜃𝜑) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wnan 1595
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 197  df-an 383  df-nan 1596
This theorem is referenced by:  nic-isw1  1753  nic-isw2  1754  nic-bijust  1760  nic-luk1  1764
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