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| 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 12243 | . 2 ⊢ 3 ∈ ℂ | |
| 2 | 1 | elexi 3467 | 1 ⊢ 3 ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2109 Vcvv 3444 ℂcc 11042 3c3 12218 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2008 ax-8 2111 ax-9 2119 ax-ext 2701 ax-1cn 11102 ax-addcl 11104 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2066 df-clab 2708 df-cleq 2721 df-clel 2803 df-v 3446 df-2 12225 df-3 12226 |
| This theorem is referenced by: fztpval 13523 funcnvs4 14857 iblcnlem1 25665 basellem9 26975 lgsdir2lem3 27214 axlowdimlem7 28851 axlowdimlem8 28852 axlowdimlem9 28853 axlowdimlem13 28857 3wlkdlem4 30064 3pthdlem1 30066 upgr4cycl4dv4e 30087 konigsberglem4 30157 konigsberglem5 30158 ex-pss 30330 ex-fv 30345 ex-1st 30346 ex-2nd 30347 rabren3dioph 42776 lhe4.4ex1a 44291 nnsum4primesodd 47770 nnsum4primesoddALTV 47771 usgrexmpl1lem 47985 usgrexmpl2lem 47990 usgrexmpl2nb0 47995 usgrexmpl2nb1 47996 usgrexmpl2nb2 47997 usgrexmpl2nb3 47998 usgrexmpl2nb4 47999 usgrexmpl2trifr 48001 zlmodzxzldeplem 48460 |
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