Theorem biorfiOLD 422

Description: Obsolete proof of biorfi 421 as of 16-Jul-2021. (Contributed by NM, 23-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
biorfi.1	⊢ ¬ 𝜑

Assertion

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

Proof of Theorem biorfiOLD

Step	Hyp	Ref	Expression
1		biorfi.1	. 2 ⊢ ¬ 𝜑
2		orc 399	. . 3 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3		orel2 397	. . 3 ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓))
4	2, 3	impbid2 215	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜓 ∨ 𝜑)))
5	1, 4	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜓 ∨ 𝜑))

Syntax hints:  ¬ wn 3   ↔ 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: (None)