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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 11095 | . 2 ⊢ 3 ∈ ℂ | |
2 | 1 | elexi 3213 | 1 ⊢ 3 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 Vcvv 3200 ℂcc 9934 3c3 11071 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-i2m1 10004 ax-1ne0 10005 ax-rrecex 10008 ax-cnre 10009 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-2 11079 df-3 11080 |
This theorem is referenced by: fztpval 12402 funcnvs4 13660 iblcnlem1 23554 basellem9 24815 lgsdir2lem3 25052 axlowdimlem7 25828 axlowdimlem13 25834 3wlkdlem4 27022 3pthdlem1 27024 upgr4cycl4dv4e 27045 konigsberglem4 27117 konigsberglem5 27118 ex-pss 27285 ex-fv 27300 rabren3dioph 37379 lhe4.4ex1a 38528 nnsum4primesodd 41684 nnsum4primesoddALTV 41685 zlmodzxzldeplem 42287 |
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