Theorem bj-biorfi 31741

Description: This should be labeled "biorfi" while the current biorfi 421 should be labeled "biorfri". The dual of biorf 419 is not biantr 968 but iba 523 (and ibar 524). 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 419	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

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:  bj-falor  31742