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Theorem nic-iimp1 1447
Description: Inference version of nic-imp 1440 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 (χ ψ))
nic-iimp1.2 (θ χ)
Assertion
Ref Expression
nic-iimp1 (θ φ)

Proof of Theorem nic-iimp1
StepHypRef Expression
1 nic-iimp1.2 . . 3 (θ χ)
2 nic-iimp1.1 . . . 4 (φ (χ ψ))
32nic-imp 1440 . . 3 ((θ χ) ((φ θ) (φ θ)))
41, 3nic-mp 1436 . 2 (φ θ)
54nic-isw1 1445 1 (θ φ)
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-iimp2  1448  nic-bi1  1453  nic-bi2  1454  nic-luk2  1457  nic-luk3  1458
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