Theorem biort 949

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

Assertion

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

Proof of Theorem biort

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (𝜑 → 𝜑)
2		orc 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
3	1, 2	2thd 268	1 ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  pm5.55  963