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Theorem nic-bi1 1761
Description: Inference to extract one side of an implication from a definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-bi1.1 ((𝜑𝜓) ⊼ ((𝜑𝜑) ⊼ (𝜓𝜓)))
Assertion
Ref Expression
nic-bi1 (𝜑 ⊼ (𝜓𝜓))

Proof of Theorem nic-bi1
StepHypRef Expression
1 nic-bi1.1 . . . 4 ((𝜑𝜓) ⊼ ((𝜑𝜑) ⊼ (𝜓𝜓)))
2 nic-id 1751 . . . 4 (𝜑 ⊼ (𝜑𝜑))
31, 2nic-iimp1 1755 . . 3 (𝜑 ⊼ (𝜑𝜓))
43nic-isw2 1754 . 2 (𝜑 ⊼ (𝜓𝜑))
54nic-idel 1757 1 (𝜑 ⊼ (𝜓𝜓))
Colors of variables: wff setvar class
Syntax hints:  wnan 1595
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 1596
This theorem is referenced by:  nic-luk1  1764  nic-luk2  1765  nic-luk3  1766
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