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Mirrors > Home > MPE Home > Th. List > 3ex | Structured version Visualization version GIF version |
Description: 3 is a set (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
3ex | ⊢ 3 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3cn 10972 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | elexi 3186 | 1 ⊢ 3 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 Vcvv 3173 ℂcc 9813 3c3 10948 |
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 df-3 10957 |
This theorem is referenced by: fztpval 12272 funcnvs4 13510 iblcnlem1 23360 basellem9 24615 lgsdir2lem3 24852 axlowdimlem7 25628 axlowdimlem13 25634 constr3lem4 26175 ex-pss 26677 ex-fv 26692 rabren3dioph 36397 lhe4.4ex1a 37550 nnsum4primesodd 40212 nnsum4primesoddALTV 40213 31wlkdlem4 41329 3pthdlem1 41331 upgr4cycl4dv4e 41352 konigsberglem4 41425 konigsberglem5 41426 zlmodzxzldeplem 42081 |
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