![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > notnot | Structured version Visualization version GIF version |
Description: Double negation introduction. Converse of notnotr 130 and one implication of notnotb 315. 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 139 | 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 143 notnotd 144 con1d 145 notnotb 315 pm2.13 897 biortn 937 necon2ad 2956 necon4ad 2960 necon4ai 2973 eueq2 3707 ifnot 4581 spthcycl 34120 knoppndvlem10 35397 wl-orel12 36380 cnfn1dd 36960 cnfn2dd 36961 axfrege41 42595 vk15.4j 43289 zfregs2VD 43602 vk15.4jVD 43675 con3ALTVD 43677 stoweidlem39 44755 |
Copyright terms: Public domain | W3C validator |