Theorem 0cnALT3 41866

Description: Alternate proof of 0cn 11244 using ax-resscn 11203, ax-addrcl 11207, ax-rnegex 11217, ax-cnre 11219 instead of ax-icn 11205, ax-addcl 11206, ax-mulcl 11208, ax-i2m1 11214. Version of 0cnALT 11486 using ax-1cn 11204 instead of ax-icn 11205. (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 11254	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11266	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2098  ℂcc 11144  0cc0 11146

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699  ax-resscn 11203  ax-1cn 11204  ax-addrcl 11207  ax-rnegex 11217  ax-cnre 11219

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rex 3068  df-v 3475  df-in 3956  df-ss 3966

This theorem is referenced by: (None)