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Mirrors > Home > ILE Home > Th. List > 2cnd | GIF version |
Description: 2 is a complex number, deductive form (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
2cnd | ⊢ (𝜑 → 2 ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8919 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | a1i 9 | 1 ⊢ (𝜑 → 2 ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 ℂcc 7742 2c2 8899 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-resscn 7836 ax-1re 7838 ax-addrcl 7841 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 df-2 8907 |
This theorem is referenced by: cnm2m1cnm3 9099 xp1d2m1eqxm1d2 9100 nneo 9285 zeo2 9288 2tnp1ge0ge0 10226 flhalf 10227 q2txmodxeq0 10309 mulbinom2 10560 binom3 10561 zesq 10562 sqoddm1div8 10597 cvg1nlemcxze 10910 resqrexlemover 10938 resqrexlemlo 10941 resqrexlemcalc1 10942 resqrexlemnm 10946 amgm2 11046 maxabslemab 11134 maxabslemlub 11135 max0addsup 11147 minabs 11163 bdtri 11167 trirecip 11428 geo2sum 11441 ege2le3 11598 efgt0 11611 tanval3ap 11641 even2n 11796 oddm1even 11797 oddp1even 11798 mulsucdiv2z 11807 ltoddhalfle 11815 m1exp1 11823 nn0enne 11824 flodddiv4 11856 flodddiv4t2lthalf 11859 sqrt2irrlem 12072 sqrt2irr 12073 pw2dvdslemn 12076 pw2dvdseulemle 12078 oddpwdc 12085 sqrt2irraplemnn 12090 prmdiv 12146 pythagtriplem15 12189 pythagtriplem16 12190 pythagtriplem17 12191 oddennn 12268 evenennn 12269 sin0pilem2 13250 cvgcmp2nlemabs 13752 trilpolemisumle 13758 apdifflemr 13767 apdiff 13768 |
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