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Theorem nic-iimp2 1755
Description: Inference version of nic-imp 1747 using left-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-iimp2.1 ((𝜑𝜓) ⊼ (𝜒𝜒))
nic-iimp2.2 (𝜃𝜑)
Assertion
Ref Expression
nic-iimp2 (𝜃 ⊼ (𝜒𝜒))

Proof of Theorem nic-iimp2
StepHypRef Expression
1 nic-iimp2.1 . . 3 ((𝜑𝜓) ⊼ (𝜒𝜒))
21nic-isw1 1752 . 2 ((𝜒𝜒) ⊼ (𝜑𝜓))
3 nic-iimp2.2 . 2 (𝜃𝜑)
42, 3nic-iimp1 1754 1 (𝜃 ⊼ (𝜒𝜒))
Colors of variables: wff setvar class
Syntax hints:  wnan 1594
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 1595
This theorem is referenced by:  nic-luk3  1765
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