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Theorem stabnot 801
Description: Every negated formula is stable. (Contributed by David A. Wheeler, 13-Aug-2018.)
Assertion
Ref Expression
stabnot STAB ¬ 𝜑

Proof of Theorem stabnot
StepHypRef Expression
1 notnotnot 606 . . 3 (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
21biimpi 119 . 2 (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3 df-stab 799 . 2 (STAB ¬ 𝜑 ↔ (¬ ¬ ¬ 𝜑 → ¬ 𝜑))
42, 3mpbir 145 1 STAB ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  STAB wstab 798
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587
This theorem depends on definitions:  df-bi 116  df-stab 799
This theorem is referenced by:  dcnn  816
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