Theorem biorfi 938

Description: The dual of biorf 936 is not biantr 805 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.)

Hypothesis

Ref	Expression
biorfi.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
biorfi	⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Proof of Theorem biorfi

Step	Hyp	Ref	Expression
1		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 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:  biorfri  939  opthprc  5731  frxp2  8152  bj-falor  36526  usgrexmpl2nb1  47937  usgrexmpl2nb2  47938  usgrexmpl2nb4  47940  usgrexmpl2nb5  47941  gpg5nbgrvtx03starlem1  47970  gpg5nbgrvtx03starlem2  47971  gpg5nbgrvtx03starlem3  47972  gpg5nbgrvtx13starlem1  47973  gpg5nbgrvtx13starlem2  47974  gpg5nbgrvtx13starlem3  47975