Theorem bj-biorfi 35450

Description: This should be labeled "biorfi" while the current biorfi 938 should be labeled "biorfri". The dual of biorf 936 is not biantr 805 but iba 529 (and ibar 530). So there should also be a "biorfr". (Note that these four statements can actually be strengthened to biconditionals.) (Contributed by BJ, 26-Oct-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-biorfi.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
bj-biorfi	⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Proof of Theorem bj-biorfi

Step	Hyp	Ref	Expression
1		bj-biorfi.1	. 2 ⊢ ¬ 𝜑
2		biorf 936	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 846

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 206  df-or 847

This theorem is referenced by:  bj-falor  35451