NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nic-swap GIF version

Theorem nic-swap 1444
Description: is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-swap ((θ φ) ((φ θ) (φ θ)))

Proof of Theorem nic-swap
StepHypRef Expression
1 nic-id 1443 . 2 (φ (φ φ))
2 nic-ax 1438 . 2 ((φ (φ φ)) ((τ (τ τ)) ((θ φ) ((φ θ) (φ θ)))))
31, 2nic-mp 1436 1 ((θ φ) ((φ θ) (φ θ)))
Colors of variables: wff setvar class
Syntax hints:   wnan 1287
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 177  df-an 360  df-nan 1288
This theorem is referenced by:  nic-isw1  1445  nic-isw2  1446  nic-bijust  1452  nic-luk1  1456
  Copyright terms: Public domain W3C validator