Theorem bj-biorfi 34692

Description: This should be labeled "biorfi" while the current biorfi 935 should be labeled "biorfri". The dual of biorf 933 is not biantr 802 but iba 527 (and ibar 528). 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 933	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 843

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 844

This theorem is referenced by:  bj-falor  34693