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Theorem dned 24
Description: Double negation elimination.
Hypothesis
Ref Expression
dned.1 (𝜑 ⅋ ~ ~ 𝜓)
Assertion
Ref Expression
dned (𝜑𝜓)

Proof of Theorem dned
StepHypRef Expression
1 dned.1 . 2 (𝜑 ⅋ ~ ~ 𝜓)
2 ax-init 7 . . . . 5 (~ 𝜓𝜓)
32mdcoi 12 . . . 4 (𝜓 ⅋ ~ 𝜓)
43dnid 23 . . 3 (𝜓 ⅋ ~ ~ ~ 𝜓)
54mdcoi 12 . 2 (~ ~ ~ 𝜓𝜓)
61, 5ax-cut 6 1 (𝜑𝜓)
Colors of variables: wff var nilad
Syntax hints:  wmd 2  ~ wneg 3
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8
This theorem is referenced by:  dne1  26  abs1  178
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