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Theorem nic-id 1750
Description: Theorem id 22 expressed with . (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-id (𝜏 ⊼ (𝜏𝜏))

Proof of Theorem nic-id
StepHypRef Expression
1 nic-ax 1745 . . 3 ((𝜓 ⊼ (𝜓𝜓)) ⊼ ((𝜃 ⊼ (𝜃𝜃)) ⊼ ((𝜑𝜓) ⊼ ((𝜓𝜑) ⊼ (𝜓𝜑)))))
21nic-idlem2 1749 . 2 ((((𝜑𝜓) ⊼ ((𝜓𝜑) ⊼ (𝜓𝜑))) ⊼ (𝜒 ⊼ (𝜒𝜒))) ⊼ (𝜓 ⊼ (𝜓𝜓)))
3 nic-idlem1 1748 . . 3 (((𝜒 ⊼ (𝜒𝜒)) ⊼ (𝜏 ⊼ (𝜏𝜏))) ⊼ ((((𝜑𝜓) ⊼ ((𝜓𝜑) ⊼ (𝜓𝜑))) ⊼ (𝜒 ⊼ (𝜒𝜒))) ⊼ (((𝜑𝜓) ⊼ ((𝜓𝜑) ⊼ (𝜓𝜑))) ⊼ (𝜒 ⊼ (𝜒𝜒)))))
43nic-idlem2 1749 . 2 (((((𝜑𝜓) ⊼ ((𝜓𝜑) ⊼ (𝜓𝜑))) ⊼ (𝜒 ⊼ (𝜒𝜒))) ⊼ (𝜓 ⊼ (𝜓𝜓))) ⊼ ((𝜒 ⊼ (𝜒𝜒)) ⊼ (𝜏 ⊼ (𝜏𝜏))))
52, 4nic-mp 1743 1 (𝜏 ⊼ (𝜏𝜏))
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-swap  1751  nic-idel  1756  nic-bi1  1760  nic-bi2  1761  nic-luk2  1764  nic-luk3  1765
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