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Theorem biorfriOLD 939
Description: Obsolete proof of biorfri 938 as of 10-Aug-2025. A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 16-Jul-2021.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
biorfi.1 ¬ 𝜑
Assertion
Ref Expression
biorfriOLD (𝜓 ↔ (𝜓𝜑))

Proof of Theorem biorfriOLD
StepHypRef Expression
1 orc 866 . 2 (𝜓 → (𝜓𝜑))
2 biorfi.1 . . 3 ¬ 𝜑
3 pm2.53 850 . . 3 ((𝜓𝜑) → (¬ 𝜓𝜑))
42, 3mt3i 149 . 2 ((𝜓𝜑) → 𝜓)
51, 4impbii 209 1 (𝜓 ↔ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 206  wo 846
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 847
This theorem is referenced by: (None)
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