Theorem 0cnALT3 42869

Description: Alternate proof of 0cn 11171 using ax-resscn 11130, ax-addrcl 11134, ax-rnegex 11144, ax-cnre 11146 instead of ax-icn 11132, ax-addcl 11133, ax-mulcl 11135, ax-i2m1 11141. Version of 0cnALT 11418 using ax-1cn 11131 instead of ax-icn 11132. (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 11183	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11196	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2142  ℂcc 11071  0cc0 11073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-resscn 11130  ax-1cn 11131  ax-addrcl 11134  ax-rnegex 11144  ax-cnre 11146

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-cleq 2754  df-clel 2837  df-rex 3087  df-ss 3921

This theorem is referenced by: (None)