Theorem biort 936

Description: A wff disjoined with truth is true. (Contributed by NM, 23-May-1999.)

Assertion

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

Proof of Theorem biort

Step	Hyp	Ref	Expression
1		orc 399	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		ax-1 6	. 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑))
3	1, 2	impbid2 215	1 ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 195   ∨ wo 382

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-or 384

This theorem is referenced by:  pm5.55  937