Theorem biorfi 952

Description: The dual of biorf 950 is not biantr 818 but iba 537 (and ibar 538). 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 950	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  biorfri  953  opthprc  5727  frxp2  8146  bj-falor  37236  usgrexmpl2nb1  48857  usgrexmpl2nb2  48858  usgrexmpl2nb4  48860  usgrexmpl2nb5  48861  gpg5nbgrvtx03starlem1  48893  gpg5nbgrvtx03starlem2  48894  gpg5nbgrvtx03starlem3  48895  gpg5nbgrvtx13starlem1  48896  gpg5nbgrvtx13starlem2  48897  gpg5nbgrvtx13starlem3  48898  gpg5edgnedg  48955