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

Theorem nic-imp 1440
 Description: Inference for nic-mp 1436 using nic-ax 1438 as major premise. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-imp.1 (φ (χ ψ))
Assertion
Ref Expression
nic-imp ((θ χ) ((φ θ) (φ θ)))

Proof of Theorem nic-imp
StepHypRef Expression
1 nic-imp.1 . 2 (φ (χ ψ))
2 nic-ax 1438 . 2 ((φ (χ ψ)) ((τ (τ τ)) ((θ χ) ((φ θ) (φ θ)))))
31, 2nic-mp 1436 1 ((θ χ) ((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-idlem1  1441  nic-idlem2  1442  nic-isw2  1446  nic-iimp1  1447  nic-idel  1449  nic-ich  1450  nic-idbl  1451  nic-luk1  1456
 Copyright terms: Public domain W3C validator