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Mirrors > Home > MPE Home > Th. List > 3ex | Structured version Visualization version GIF version |
Description: 3 is a set. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
3ex | ⊢ 3 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3cn 11287 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | elexi 3353 | 1 ⊢ 3 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2139 Vcvv 3340 ℂcc 10126 3c3 11263 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-9 2148 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 ax-ext 2740 ax-resscn 10185 ax-1cn 10186 ax-icn 10187 ax-addcl 10188 ax-addrcl 10189 ax-mulcl 10190 ax-mulrcl 10191 ax-i2m1 10196 ax-1ne0 10197 ax-rrecex 10200 ax-cnre 10201 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1074 df-tru 1635 df-ex 1854 df-nf 1859 df-sb 2047 df-clab 2747 df-cleq 2753 df-clel 2756 df-nfc 2891 df-ne 2933 df-ral 3055 df-rex 3056 df-rab 3059 df-v 3342 df-dif 3718 df-un 3720 df-in 3722 df-ss 3729 df-nul 4059 df-if 4231 df-sn 4322 df-pr 4324 df-op 4328 df-uni 4589 df-br 4805 df-iota 6012 df-fv 6057 df-ov 6816 df-2 11271 df-3 11272 |
This theorem is referenced by: fztpval 12595 funcnvs4 13860 iblcnlem1 23753 basellem9 25014 lgsdir2lem3 25251 axlowdimlem7 26027 axlowdimlem13 26033 3wlkdlem4 27314 3pthdlem1 27316 upgr4cycl4dv4e 27337 konigsberglem4 27407 konigsberglem5 27408 ex-pss 27596 ex-fv 27611 rabren3dioph 37881 lhe4.4ex1a 39030 nnsum4primesodd 42194 nnsum4primesoddALTV 42195 zlmodzxzldeplem 42797 |
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