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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 316. 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 316 pm2.13 892 biortn 932 necon2ad 2999 necon4ad 3003 necon4ai 3015 eueq2 3637 ifnot 4431 spthcycl 31985 knoppndvlem10 33470 wl-orel12 34301 cnfn1dd 34921 cnfn2dd 34922 axfrege41 39694 vk15.4j 40420 zfregs2VD 40733 vk15.4jVD 40806 con3ALTVD 40808 stoweidlem39 41886 |
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