Theorem recni 7421

Description: A real number is a complex number. (Contributed by NM, 1-Mar-1995.)

Hypothesis

Ref	Expression
recni.1	|- A e. RR

Assertion

Ref	Expression
recni	|- A e. CC

Proof of Theorem recni

Step	Hyp	Ref	Expression
1		ax-resscn 7358	. 2 |- RR C_ CC
2		recni.1	. 2 |- A e. RR
3	1, 2	sselii 3009	1 |- A e. CC

Syntax hints:   e. wcel 1436   CCcc 7269   RRcr 7270

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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-resscn 7358

This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-in 2992  df-ss 2999

This theorem is referenced by:  resubcli  7666  ltapii  8028  nncni  8344  2cn  8405  3cn  8409  4cn  8412  5cn  8414  6cn  8416  7cn  8418  8cn  8420  9cn  8422  halfcn  8540  8th4div3  8545  nn0cni  8595  numltc  8811  sqge0i  9892  lt2sqi  9893  le2sqi  9894  sq11i  9895  sqrtmsq2i  10409  sqrt2irraplemnn  10951