Metamath Proof Explorer

Theorem wl-luk-id

Description: Principle of identity. Theorem *2.08 of WhiteheadRussell p. 101. Copy of id with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	wl-luk-id	⊢ ( 𝜑 → 𝜑 )

Proof

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