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Theorem biorfi 675
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)
Hypothesis
Ref Expression
biorfi.1 ¬ 𝜑
Assertion
Ref Expression
biorfi (𝜓 ↔ (𝜓𝜑))

Proof of Theorem biorfi
StepHypRef Expression
1 biorfi.1 . 2 ¬ 𝜑
2 orc 643 . . 3 (𝜓 → (𝜓𝜑))
3 orel2 655 . . 3 𝜑 → ((𝜓𝜑) → 𝜓))
42, 3impbid2 135 . 2 𝜑 → (𝜓 ↔ (𝜓𝜑)))
51, 4ax-mp 7 1 (𝜓 ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  pm4.43  867  dn1dc  878  excxor  1285  un0  3279  opthprc  4419  frec0g  6014  dcdc  10288
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