Theorem 0cnALT3 41176

Description: Alternate proof of 0cn 11205 using ax-resscn 11166, ax-addrcl 11170, ax-rnegex 11180, ax-cnre 11182 instead of ax-icn 11168, ax-addcl 11169, ax-mulcl 11171, ax-i2m1 11177. Version of 0cnALT 11447 using ax-1cn 11167 instead of ax-icn 11168. (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

Step	Hyp	Ref	Expression
1		0re 11215	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11227	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2106  ℂcc 11107  0cc0 11109

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-resscn 11166  ax-1cn 11167  ax-addrcl 11170  ax-rnegex 11180  ax-cnre 11182

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rex 3071  df-v 3476  df-in 3955  df-ss 3965

This theorem is referenced by: (None)