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Mirrors > Home > MPE Home > Th. List > 2ex | Structured version Visualization version GIF version |
Description: 2 is a set (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
2ex | ⊢ 2 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 10968 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | elexi 3186 | 1 ⊢ 2 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 Vcvv 3173 ℂcc 9813 2c2 10947 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-resscn 9872 ax-1cn 9873 ax-icn 9874 ax-addcl 9875 ax-addrcl 9876 ax-mulcl 9877 ax-mulrcl 9878 ax-i2m1 9883 ax-1ne0 9884 ax-rrecex 9887 ax-cnre 9888 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-2 10956 |
This theorem is referenced by: fzprval 12271 fztpval 12272 funcnvs3 13509 funcnvs4 13510 wrd3tpop 13539 wrdl3s3 13553 pmtrprfval 17730 m2detleiblem3 20254 m2detleiblem4 20255 iblcnlem1 23360 gausslemma2dlem4 24894 2lgslem4 24931 selberglem1 25034 axlowdimlem4 25625 wlkntrllem2 26090 2pthlem2 26126 constr3lem2 26174 constr3lem4 26175 constr3lem5 26176 constr3trllem1 26178 eupath 26508 ex-ima 26691 rabren3dioph 36397 refsum2cnlem1 38219 nnsum3primes4 40204 nnsum3primesgbe 40208 nnsum4primesodd 40212 nnsum4primesoddALTV 40213 21wlkdlem4 41135 2pthdlem1 41137 umgrwwlks2on 41161 31wlkdlem4 41329 31wlkdlem5 41330 3pthdlem1 41331 31wlkdlem10 41336 upgr3v3e3cycl 41347 upgr4cycl4dv4e 41352 eulerpathpr 41408 zlmodzxzldeplem3 42085 zlmodzxzldeplem4 42086 |
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