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Theorem recni 7479
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 7416 . 2 ℝ ⊆ ℂ
2 recni.1 . 2 𝐴 ∈ ℝ
31, 2sselii 3020 1 𝐴 ∈ ℂ
Colors of variables: wff set class
Syntax hints:  wcel 1438  cc 7327  cr 7328
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-resscn 7416
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010
This theorem is referenced by:  resubcli  7724  ltapii  8086  nncni  8404  2cn  8464  3cn  8468  4cn  8471  5cn  8473  6cn  8475  7cn  8477  8cn  8479  9cn  8481  halfcn  8600  8th4div3  8605  nn0cni  8655  numltc  8871  sqge0i  10006  lt2sqi  10007  le2sqi  10008  sq11i  10009  sqrtmsq2i  10533  0.999...  10876  sqrt2irraplemnn  11250
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