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Theorem biortn 735
Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)
Assertion
Ref Expression
biortn (𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))

Proof of Theorem biortn
StepHypRef Expression
1 notnot 619 . 2 (𝜑 → ¬ ¬ 𝜑)
2 biorf 734 . 2 (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
31, 2syl 14 1 (𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104  wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  oranabs  805
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