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Mirrors > Home > LLPE Home > Th. List > dned | Structured version |
Description: Double negation elimination. |
Ref | Expression |
---|---|
dned.1 | ⊦ (𝜑 ⅋ ~ ~ 𝜓) |
Ref | Expression |
---|---|
dned | ⊦ (𝜑 ⅋ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dned.1 | . 2 ⊦ (𝜑 ⅋ ~ ~ 𝜓) | |
2 | ax-init 7 | . . . . 5 ⊦ (~ 𝜓 ⅋ 𝜓) | |
3 | 2 | mdcoi 12 | . . . 4 ⊦ (𝜓 ⅋ ~ 𝜓) |
4 | 3 | dnid 23 | . . 3 ⊦ (𝜓 ⅋ ~ ~ ~ 𝜓) |
5 | 4 | mdcoi 12 | . 2 ⊦ (~ ~ ~ 𝜓 ⅋ 𝜓) |
6 | 1, 5 | ax-cut 6 | 1 ⊦ (𝜑 ⅋ 𝜓) |
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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