ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  7cn GIF version

Theorem 7cn 8797
Description: The number 7 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
7cn 7 ∈ ℂ

Proof of Theorem 7cn
StepHypRef Expression
1 7re 8796 . 2 7 ∈ ℝ
21recni 7771 1 7 ∈ ℂ
Colors of variables: wff set class
Syntax hints:  wcel 1480  cc 7611  7c7 8769
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  df-3 8773  df-4 8774  df-5 8775  df-6 8776  df-7 8777
This theorem is referenced by:  8m1e7  8838  7p2e9  8864  7p3e10  9249  7t2e14  9283  7t4e28  9285  7t7e49  9288  cos2bnd  11456
  Copyright terms: Public domain W3C validator