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Metamath Proof Explorer

Theorem oridm

Description: Idempotent law for disjunction. Theorem *4.25 of WhiteheadRussell p. 117. (Contributed by NM, 11-May-1993) (Proof shortened by Andrew Salmon, 16-Apr-2011) (Proof shortened by Wolf Lammen, 10-Mar-2013)

		Ref	Expression
	Assertion	oridm	⊢ ( ( 𝜑 ∨ 𝜑 ) ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm1.2	⊢ ( ( 𝜑 ∨ 𝜑 ) → 𝜑 )
2		pm2.07	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜑 ) )
3	1 2	impbii	⊢ ( ( 𝜑 ∨ 𝜑 ) ↔ 𝜑 )