Theorem biort 830

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 19	. 2 ⊢ (𝜑 → 𝜑)
2		orc 713	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
3	1, 2	2thd 175	1 ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 105   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.55dc  914