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Mirrors > Home > MPE Home > Th. List > notnotd | Structured version Visualization version GIF version |
Description: Deduction associated with notnot 135 and notnoti 136. (Contributed by Jarvin Udandy, 2-Sep-2016.) Avoid biconditional. (Revised by Wolf Lammen, 27-Mar-2021.) |
Ref | Expression |
---|---|
notnotd.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
notnotd | ⊢ (𝜑 → ¬ ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotd.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | notnot 135 | . 2 ⊢ (𝜓 → ¬ ¬ 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ¬ ¬ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: cusgrares 26001 uvtx01vtx 26020 xrdifh 28932 amosym1 31595 nnfoctbdjlem 39348 lighneallem1 40060 lighneallem3 40062 eupth2lemb 41405 lindslinindsimp2 42046 |
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