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  5715  frxp2  8161  bj-falor  37454  usgrexmpl2nb1  49129  usgrexmpl2nb2  49130  usgrexmpl2nb4  49132  usgrexmpl2nb5  49133  gpg5nbgrvtx03starlem1  49165  gpg5nbgrvtx03starlem2  49166  gpg5nbgrvtx03starlem3  49167  gpg5nbgrvtx13starlem1  49168  gpg5nbgrvtx13starlem2  49169  gpg5nbgrvtx13starlem3  49170  gpg5edgnedg  49227