Theorem 0cnALT3 42226

Description: Alternate proof of 0cn 11107 using ax-resscn 11066, ax-addrcl 11070, ax-rnegex 11080, ax-cnre 11082 instead of ax-icn 11068, ax-addcl 11069, ax-mulcl 11071, ax-i2m1 11077. Version of 0cnALT 11351 using ax-1cn 11067 instead of ax-icn 11068. (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 11117	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11129	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2109  ℂcc 11007  0cc0 11009

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-resscn 11066  ax-1cn 11067  ax-addrcl 11070  ax-rnegex 11080  ax-cnre 11082

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2721  df-clel 2803  df-rex 3054  df-ss 3920

This theorem is referenced by: (None)