Theorem biorfriOLD 940

Description: Obsolete version of biorfri 939 as of 10-Aug-2025. A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 16-Jul-2021.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
biorfi.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
biorfriOLD	⊢ (𝜓 ↔ (𝜓 ∨ 𝜑))

Proof of Theorem biorfriOLD

Step	Hyp	Ref	Expression
1		orc 867	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
2		biorfi.1	. . 3 ⊢ ¬ 𝜑
3		pm2.53 851	. . 3 ⊢ ((𝜓 ∨ 𝜑) → (¬ 𝜓 → 𝜑))
4	2, 3	mt3i 149	. 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜓)
5	1, 4	impbii 209	1 ⊢ (𝜓 ↔ (𝜓 ∨ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 206   ∨ wo 847

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 207  df-or 848

This theorem is referenced by: (None)