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Theorem recni 7039
 Description: A real number is a complex number. (Contributed by NM, 1-Mar-1995.)
Hypothesis
Ref Expression
recni.1 𝐴 ∈ ℝ
Assertion
Ref Expression
recni 𝐴 ∈ ℂ

Proof of Theorem recni
StepHypRef Expression
1 ax-resscn 6976 . 2 ℝ ⊆ ℂ
2 recni.1 . 2 𝐴 ∈ ℝ
31, 2sselii 2942 1 𝐴 ∈ ℂ
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  ℂcc 6887  ℝcr 6888 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  resubcli  7274  ltapii  7624  nncni  7924  2cn  7986  3cn  7990  4cn  7993  5cn  7995  6cn  7997  7cn  7999  8cn  8001  9cn  8003  halfcn  8139  8th4div3  8144  nn0cni  8193  numltc  8387  sqge0i  9340  lt2sqi  9341  le2sqi  9342  sq11i  9343  sqrtmsq2i  9731
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