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Mirrors > Home > ILE Home > Th. List > 4cn | GIF version |
Description: The number 4 is a complex number. (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
4cn | ⊢ 4 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4re 9027 | . 2 ⊢ 4 ∈ ℝ | |
2 | 1 | recni 8000 | 1 ⊢ 4 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 ℂcc 7840 4c4 9003 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-resscn 7934 ax-1re 7936 ax-addrcl 7939 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 df-2 9009 df-3 9010 df-4 9011 |
This theorem is referenced by: 5m1e4 9072 4p2e6 9093 4p3e7 9094 4p4e8 9095 4t2e8 9108 4d2e2 9110 8th4div3 9169 div4p1lem1div2 9203 5p5e10 9485 4t4e16 9513 6t5e30 9521 fzo0to42pr 10252 fldiv4p1lem1div2 10338 sq4e2t8 10652 sqoddm1div8 10708 4bc3eq4 10788 4bc2eq6 10789 resqrexlemover 11054 resqrexlemcalc1 11058 resqrexlemcalc3 11060 cos2bnd 11803 flodddiv4 11974 6gcd4e2 12031 6lcm4e12 12122 pythagtriplem1 12300 dveflem 14664 sincosq4sgn 14727 cosq23lt0 14731 sincos6thpi 14740 2lgsoddprmlem2 14932 2lgsoddprmlem3c 14935 2lgsoddprmlem3d 14936 ex-exp 14957 ex-fac 14958 ex-bc 14959 |
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