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Theorem nic-stdmp 1762
 Description: Derive the standard modus ponens from nic-mp 1743. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-smin 𝜑
nic-smaj (𝜑𝜓)
Assertion
Ref Expression
nic-stdmp 𝜓

Proof of Theorem nic-stdmp
StepHypRef Expression
1 nic-smin . 2 𝜑
2 nic-smaj . . 3 (𝜑𝜓)
3 nic-dfim 1741 . . . 4 (((𝜑 ⊼ (𝜓𝜓)) ⊼ (𝜑𝜓)) ⊼ (((𝜑 ⊼ (𝜓𝜓)) ⊼ (𝜑 ⊼ (𝜓𝜓))) ⊼ ((𝜑𝜓) ⊼ (𝜑𝜓))))
43nic-bi2 1761 . . 3 ((𝜑𝜓) ⊼ ((𝜑 ⊼ (𝜓𝜓)) ⊼ (𝜑 ⊼ (𝜓𝜓))))
52, 4nic-mp 1743 . 2 (𝜑 ⊼ (𝜓𝜓))
61, 5nic-mp 1743 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊼ 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-or 827  df-nan 1595 This theorem is referenced by: (None)
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