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Theorem wl-id 32244
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-id (𝜑𝜑)

Proof of Theorem wl-id
StepHypRef Expression
1 ax-luk3 32222 . 2 (𝜑 → (¬ 𝜑𝜑))
2 ax-luk2 32221 . 2 ((¬ 𝜑𝜑) → 𝜑)
31, 2wl-syl 32225 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 32220  ax-luk2 32221  ax-luk3 32222
This theorem is referenced by:  wl-notnotr  32245
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