Theorem wl-luk-id 34718

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	⊢ (𝜑 → 𝜑)

Proof of Theorem wl-luk-id

Step	Hyp	Ref	Expression
1		ax-luk3 34696	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜑))
2		ax-luk2 34695	. 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)
3	1, 2	wl-luk-syl 34699	1 ⊢ (𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 34694  ax-luk2 34695  ax-luk3 34696

This theorem is referenced by:  wl-luk-notnotr  34719