Theorem 0cnALT3 40211

Description: Alternate proof of 0cn 10898 using ax-resscn 10859, ax-addrcl 10863, ax-rnegex 10873, ax-cnre 10875 instead of ax-icn 10861, ax-addcl 10862, ax-mulcl 10864, ax-i2m1 10870. Version of 0cnALT 11139 using ax-1cn 10860 instead of ax-icn 10861. (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 10908	. 2 ⊢ 0 ∈ ℝ
2	1	recni 10920	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2108  ℂcc 10800  0cc0 10802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-resscn 10859  ax-1cn 10860  ax-addrcl 10863  ax-rnegex 10873  ax-cnre 10875

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-ral 3068  df-rex 3069  df-v 3424  df-in 3890  df-ss 3900

This theorem is referenced by: (None)