| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > 3ex | Structured version Visualization version GIF version | ||
| Description: The number 3 is a set. (Contributed by David A. Wheeler, 8-Dec-2018.) |
| Ref | Expression |
|---|---|
| 3ex | ⊢ 3 ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3cn 12253 | . 2 ⊢ 3 ∈ ℂ | |
| 2 | 1 | elexi 3453 | 1 ⊢ 3 ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2114 Vcvv 3430 ℂcc 11027 3c3 12228 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1912 ax-6 1969 ax-7 2010 ax-8 2116 ax-9 2124 ax-ext 2709 ax-1cn 11087 ax-addcl 11089 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1545 df-ex 1782 df-sb 2069 df-clab 2716 df-cleq 2729 df-clel 2812 df-v 3432 df-2 12235 df-3 12236 |
| This theorem is referenced by: fztpval 13531 funcnvs4 14868 iblcnlem1 25765 basellem9 27066 lgsdir2lem3 27304 axlowdimlem7 29031 axlowdimlem8 29032 axlowdimlem9 29033 axlowdimlem13 29037 3wlkdlem4 30247 3pthdlem1 30249 upgr4cycl4dv4e 30270 konigsberglem4 30340 konigsberglem5 30341 ex-pss 30513 ex-fv 30528 ex-1st 30529 ex-2nd 30530 rabren3dioph 43261 lhe4.4ex1a 44774 nnsum4primesodd 48284 nnsum4primesoddALTV 48285 usgrexmpl1lem 48509 usgrexmpl2lem 48514 usgrexmpl2nb0 48519 usgrexmpl2nb1 48520 usgrexmpl2nb2 48521 usgrexmpl2nb3 48522 usgrexmpl2nb4 48523 usgrexmpl2trifr 48525 zlmodzxzldeplem 48986 |
| Copyright terms: Public domain | W3C validator |