Theorem biorfi 951

Description: The dual of biorf 949 is not biantr 817 but iba 536 (and ibar 537). 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 949	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 209   ∨ wo 860

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 210  df-or 861

This theorem is referenced by:  biorfri  952  opthprc  5726  frxp2  8140  bj-falor  37100  usgrexmpl2nb1  48720  usgrexmpl2nb2  48721  usgrexmpl2nb4  48723  usgrexmpl2nb5  48724  gpg5nbgrvtx03starlem1  48756  gpg5nbgrvtx03starlem2  48757  gpg5nbgrvtx03starlem3  48758  gpg5nbgrvtx13starlem1  48759  gpg5nbgrvtx13starlem2  48760  gpg5nbgrvtx13starlem3  48761  gpg5edgnedg  48818