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Theorem biortn 651
Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)
Assertion
Ref Expression
biortn (φ → (ψ ↔ (¬ φ ψ)))

Proof of Theorem biortn
StepHypRef Expression
1 notnot1 547 . 2 (φ → ¬ ¬ φ)
2 biorf 650 . 2 (¬ ¬ φ → (ψ ↔ (¬ φ ψ)))
31, 2syl 14 1 (φ → (ψ ↔ (¬ φ ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  oranabs  716
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