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Mirrors > Home > MPE Home > Th. List > notnot | Structured version Visualization version GIF version |
Description: Double negation introduction. Converse of notnotr 132 and one implication of notnotb 317. Theorem *2.12 of [WhiteheadRussell] p. 101. This was the sixth axiom of Frege, specifically Proposition 41 of [Frege1879] p. 47. (Contributed by NM, 28-Dec-1992.) (Proof shortened by Wolf Lammen, 2-Mar-2013.) |
Ref | Expression |
---|---|
notnot | ⊢ (𝜑 → ¬ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (¬ 𝜑 → ¬ 𝜑) | |
2 | 1 | con2i 141 | 1 ⊢ (𝜑 → ¬ ¬ 𝜑) |
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: notnoti 145 notnotd 146 con1d 147 notnotb 317 pm2.13 894 biortn 934 necon2ad 3031 necon4ad 3035 necon4ai 3047 eueq2 3701 ifnot 4517 spthcycl 32371 knoppndvlem10 33855 wl-orel12 34745 cnfn1dd 35364 cnfn2dd 35365 axfrege41 40183 vk15.4j 40855 zfregs2VD 41168 vk15.4jVD 41241 con3ALTVD 41243 stoweidlem39 42317 |
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