Theorem biort

Description: A disjunction with a true formula is equivalent to that true formula. (Contributed by NM, 23-May-1999)

	Ref	Expression
Assertion	biort	⊢ ( 𝜑 → ( 𝜑 ↔ ( 𝜑 ∨ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
3	1 2	2thd	⊢ ( 𝜑 → ( 𝜑 ↔ ( 𝜑 ∨ 𝜓 ) ) )