Theorem 0cnALT3 42737

Description: Alternate proof of 0cn 11127 using ax-resscn 11086, ax-addrcl 11090, ax-rnegex 11100, ax-cnre 11102 instead of ax-icn 11088, ax-addcl 11089, ax-mulcl 11091, ax-i2m1 11097. Version of 0cnALT 11372 using ax-1cn 11087 instead of ax-icn 11088. (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 11137	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11150	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2119  ℂcc 11027  0cc0 11029

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-resscn 11086  ax-1cn 11087  ax-addrcl 11090  ax-rnegex 11100  ax-cnre 11102

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-cleq 2731  df-clel 2814  df-rex 3064  df-ss 3900

This theorem is referenced by: (None)