Theorem 7cn 9367

Description: The number 7 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
7cn	⊢ 7 ∈ ℂ

Proof of Theorem 7cn

Step	Hyp	Ref	Expression
1		7re 9366	. 2 ⊢ 7 ∈ ℝ
2	1	recni 8328	1 ⊢ 7 ∈ ℂ

Syntax hints:   ∈ wcel 2209  ℂcc 8167  7c7 9339

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-resscn 8261  ax-1re 8263  ax-addrcl 8266

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-2 9342  df-3 9343  df-4 9344  df-5 9345  df-6 9346  df-7 9347

This theorem is referenced by:  8m1e7  9408  7p2e9  9435  7p3e10  9830  7t2e14  9864  7t4e28  9866  7t7e49  9869  cos2bnd  12505  2lgslem3d  16129