Theorem 0cnALT3 42294

Description: Alternate proof of 0cn 11254 using ax-resscn 11213, ax-addrcl 11217, ax-rnegex 11227, ax-cnre 11229 instead of ax-icn 11215, ax-addcl 11216, ax-mulcl 11218, ax-i2m1 11224. Version of 0cnALT 11497 using ax-1cn 11214 instead of ax-icn 11215. (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 11264	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11276	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2107  ℂcc 11154  0cc0 11156

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-resscn 11213  ax-1cn 11214  ax-addrcl 11217  ax-rnegex 11227  ax-cnre 11229

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-cleq 2728  df-clel 2815  df-rex 3070  df-ss 3967

This theorem is referenced by: (None)