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Theorem nic-idel 1758
Description: Inference to remove the trailing term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-idel.1 (𝜑 ⊼ (𝜒𝜓))
Assertion
Ref Expression
nic-idel (𝜑 ⊼ (𝜒𝜒))

Proof of Theorem nic-idel
StepHypRef Expression
1 nic-id 1752 . . 3 (𝜒 ⊼ (𝜒𝜒))
21nic-isw1 1754 . 2 ((𝜒𝜒) ⊼ 𝜒)
3 nic-idel.1 . . 3 (𝜑 ⊼ (𝜒𝜓))
43nic-imp 1749 . 2 (((𝜒𝜒) ⊼ 𝜒) ⊼ ((𝜑 ⊼ (𝜒𝜒)) ⊼ (𝜑 ⊼ (𝜒𝜒))))
52, 4nic-mp 1745 1 (𝜑 ⊼ (𝜒𝜒))
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-bi1  1762  nic-bi2  1763  nic-luk1  1765
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