Theorem 0cnALT3 38142

Description: Alternate proof of 0cn 10368 using ax-resscn 10329, ax-addrcl 10333, ax-rnegex 10343, ax-cnre 10345 instead of ax-icn 10331, ax-addcl 10332, ax-mulcl 10334, ax-i2m1 10340. Version of 0cnALT 10610 using ax-1cn 10330 instead of ax-icn 10331. (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 10378	. 2 ⊢ 0 ∈ ℝ
2	1	recni 10391	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2107  ℂcc 10270  0cc0 10272

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754  ax-resscn 10329  ax-1cn 10330  ax-addrcl 10333  ax-rnegex 10343  ax-cnre 10345

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-ral 3095  df-rex 3096  df-in 3799  df-ss 3806

This theorem is referenced by: (None)