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Theorem wl-luk-id 34595
Description: Principle of identity. Theorem *2.08 of [WhiteheadRussell] p. 101. Copy of id 22 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-luk-id (𝜑𝜑)

Proof of Theorem wl-luk-id
StepHypRef Expression
1 ax-luk3 34573 . 2 (𝜑 → (¬ 𝜑𝜑))
2 ax-luk2 34572 . 2 ((¬ 𝜑𝜑) → 𝜑)
31, 2wl-luk-syl 34576 1 (𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 34571  ax-luk2 34572  ax-luk3 34573
This theorem is referenced by:  wl-luk-notnotr  34596
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