Theorem 0cnALT3 42911

Description: Alternate proof of 0cn 11198 using ax-resscn 11157, ax-addrcl 11161, ax-rnegex 11171, ax-cnre 11173 instead of ax-icn 11159, ax-addcl 11160, ax-mulcl 11162, ax-i2m1 11168. Version of 0cnALT 11445 using ax-1cn 11158 instead of ax-icn 11159. (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 11210	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11223	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2149  ℂcc 11098  0cc0 11100

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-resscn 11157  ax-1cn 11158  ax-addrcl 11161  ax-rnegex 11171  ax-cnre 11173

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-cleq 2761  df-clel 2844  df-rex 3096  df-ss 3930

This theorem is referenced by: (None)