Theorem 0cnALT3 42294

Description: Alternate proof of 0cn 11104 using ax-resscn 11063, ax-addrcl 11067, ax-rnegex 11077, ax-cnre 11079 instead of ax-icn 11065, ax-addcl 11066, ax-mulcl 11068, ax-i2m1 11074. Version of 0cnALT 11348 using ax-1cn 11064 instead of ax-icn 11065. (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 11114	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11126	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2111  ℂcc 11004  0cc0 11006

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-resscn 11063  ax-1cn 11064  ax-addrcl 11067  ax-rnegex 11077  ax-cnre 11079

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-cleq 2723  df-clel 2806  df-rex 3057  df-ss 3914

This theorem is referenced by: (None)