MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nic-iimp1 Structured version   Visualization version   GIF version

Theorem nic-iimp1 1756
Description: Inference version of nic-imp 1749 using right-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-iimp1.1 (𝜑 ⊼ (𝜒𝜓))
nic-iimp1.2 (𝜃𝜒)
Assertion
Ref Expression
nic-iimp1 (𝜃𝜑)

Proof of Theorem nic-iimp1
StepHypRef Expression
1 nic-iimp1.2 . . 3 (𝜃𝜒)
2 nic-iimp1.1 . . . 4 (𝜑 ⊼ (𝜒𝜓))
32nic-imp 1749 . . 3 ((𝜃𝜒) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))
41, 3nic-mp 1745 . 2 (𝜑𝜃)
54nic-isw1 1754 1 (𝜃𝜑)
Colors of variables: wff setvar class
Syntax hints:  wnan 1596
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 385  df-nan 1597
This theorem is referenced by:  nic-iimp2  1757  nic-bi1  1762  nic-bi2  1763  nic-luk2  1766  nic-luk3  1767
  Copyright terms: Public domain W3C validator