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Theorem dnes 79
Description: Double negation elimination. Syllogism form of dned 24.
Assertion
Ref Expression
dnes (~ ~ 𝜑𝜑)

Proof of Theorem dnes
StepHypRef Expression
1 ax-init 7 . . . . 5 (~ 𝜑𝜑)
21mdcoi 12 . . . 4 (𝜑 ⅋ ~ 𝜑)
3 ax-init 7 . . . . 5 (~ ~ ~ 𝜑 ⅋ ~ ~ 𝜑)
43mdcoi 12 . . . 4 (~ ~ 𝜑 ⅋ ~ ~ ~ 𝜑)
52, 4ax-cut 6 . . 3 (𝜑 ⅋ ~ ~ ~ 𝜑)
65mdcoi 12 . 2 (~ ~ ~ 𝜑𝜑)
7 df-li 62 . 2 ((~ ~ 𝜑𝜑) ⧟ (~ ~ ~ 𝜑𝜑))
86, 7lb2i 60 1 (~ ~ 𝜑𝜑)
Colors of variables: wff var nilad
Syntax hints:  wmd 2  ~ wneg 3  wli 61
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-eac1 33  ax-eac2 34
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by:  dn  107
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