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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 8784 | . 2 ⊢ 2 ∈ ℂ | |
2 | 1 | a1i 9 | 1 ⊢ (𝜑 → 2 ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1480 ℂcc 7611 2c2 8764 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 df-2 8772 |
This theorem is referenced by: cnm2m1cnm3 8964 xp1d2m1eqxm1d2 8965 nneo 9147 zeo2 9150 2tnp1ge0ge0 10067 flhalf 10068 q2txmodxeq0 10150 mulbinom2 10401 binom3 10402 zesq 10403 sqoddm1div8 10437 cvg1nlemcxze 10747 resqrexlemover 10775 resqrexlemlo 10778 resqrexlemcalc1 10779 resqrexlemnm 10783 amgm2 10883 maxabslemab 10971 maxabslemlub 10972 max0addsup 10984 minabs 11000 bdtri 11004 trirecip 11263 geo2sum 11276 ege2le3 11366 efgt0 11379 tanval3ap 11410 even2n 11560 oddm1even 11561 oddp1even 11562 mulsucdiv2z 11571 ltoddhalfle 11579 m1exp1 11587 nn0enne 11588 flodddiv4 11620 flodddiv4t2lthalf 11623 sqrt2irrlem 11828 sqrt2irr 11829 pw2dvdslemn 11832 pw2dvdseulemle 11834 oddpwdc 11841 sqrt2irraplemnn 11846 oddennn 11894 evenennn 11895 sin0pilem2 12852 cvgcmp2nlemabs 13216 trilpolemisumle 13220 |
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