Theorem 0cnALT3 42709

Description: Alternate proof of 0cn 11130 using ax-resscn 11089, ax-addrcl 11093, ax-rnegex 11103, ax-cnre 11105 instead of ax-icn 11091, ax-addcl 11092, ax-mulcl 11094, ax-i2m1 11100. Version of 0cnALT 11375 using ax-1cn 11090 instead of ax-icn 11091. (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 11140	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11153	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2114  ℂcc 11030  0cc0 11032

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-resscn 11089  ax-1cn 11090  ax-addrcl 11093  ax-rnegex 11103  ax-cnre 11105

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729  df-clel 2812  df-rex 3063  df-ss 3907

This theorem is referenced by: (None)