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Theorem biortn 921
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 138 . 2 (𝜑 → ¬ ¬ 𝜑)
2 biorf 920 . 2 (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
31, 2syl 17 1 (𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 834
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 197  df-or 835
This theorem is referenced by:  oranabs  981  xrdifh  29882  ballotlemfc0  30894  ballotlemfcc  30895  topdifinfindis  33531  topdifinffinlem  33532  4atlem3a  35405  4atlem3b  35406  ntrneineine1lem  38908
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