Theorem 0cnALT3 42273

Description: Alternate proof of 0cn 11251 using ax-resscn 11210, ax-addrcl 11214, ax-rnegex 11224, ax-cnre 11226 instead of ax-icn 11212, ax-addcl 11213, ax-mulcl 11215, ax-i2m1 11221. Version of 0cnALT 11494 using ax-1cn 11211 instead of ax-icn 11212. (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 11261	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11273	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2106  ℂcc 11151  0cc0 11153

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-resscn 11210  ax-1cn 11211  ax-addrcl 11214  ax-rnegex 11224  ax-cnre 11226

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-cleq 2727  df-clel 2814  df-rex 3069  df-ss 3980

This theorem is referenced by: (None)