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Theorem nic-iimp1 1598
 Description: Inference version of nic-imp 1591 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 1591 . . 3 ((𝜃𝜒) ⊼ ((𝜑𝜃) ⊼ (𝜑𝜃)))
41, 3nic-mp 1587 . 2 (𝜑𝜃)
54nic-isw1 1596 1 (𝜃𝜑)
 Colors of variables: wff setvar class Syntax hints:   ⊼ wnan 1439 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 196  df-an 385  df-nan 1440 This theorem is referenced by:  nic-iimp2  1599  nic-bi1  1604  nic-bi2  1605  nic-luk2  1608  nic-luk3  1609
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