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Theorem 0cnALT3 39632
 Description: Alternate proof of 0cn 10640 using ax-resscn 10601, ax-addrcl 10605, ax-rnegex 10615, ax-cnre 10617 instead of ax-icn 10603, ax-addcl 10604, ax-mulcl 10606, ax-i2m1 10612. Version of 0cnALT 10881 using ax-1cn 10602 instead of ax-icn 10603. (Contributed by Steven Nguyen, 7-Jan-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
0cnALT3 0 ∈ ℂ

Proof of Theorem 0cnALT3
StepHypRef Expression
1 0re 10650 . 2 0 ∈ ℝ
21recni 10662 1 0 ∈ ℂ
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2111  ℂcc 10542  0cc0 10544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-resscn 10601  ax-1cn 10602  ax-addrcl 10605  ax-rnegex 10615  ax-cnre 10617 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ral 3111  df-rex 3112  df-v 3444  df-in 3890  df-ss 3900 This theorem is referenced by: (None)
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