Theorem biorfi 949

Description: The dual of biorf 947 is not biantr 815 but iba 535 (and ibar 536). 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 947	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 208   ∨ wo 858

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 209  df-or 859

This theorem is referenced by:  biorfri  950  opthprc  5711  frxp2  8124  bj-falor  37027  usgrexmpl2nb1  48654  usgrexmpl2nb2  48655  usgrexmpl2nb4  48657  usgrexmpl2nb5  48658  gpg5nbgrvtx03starlem1  48690  gpg5nbgrvtx03starlem2  48691  gpg5nbgrvtx03starlem3  48692  gpg5nbgrvtx13starlem1  48693  gpg5nbgrvtx13starlem2  48694  gpg5nbgrvtx13starlem3  48695  gpg5edgnedg  48752