Theorem 0cnALT3 42241

Description: Alternate proof of 0cn 11166 using ax-resscn 11125, ax-addrcl 11129, ax-rnegex 11139, ax-cnre 11141 instead of ax-icn 11127, ax-addcl 11128, ax-mulcl 11130, ax-i2m1 11136. Version of 0cnALT 11409 using ax-1cn 11126 instead of ax-icn 11127. (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 11176	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11188	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2109  ℂcc 11066  0cc0 11068

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 11125  ax-1cn 11126  ax-addrcl 11129  ax-rnegex 11139  ax-cnre 11141

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 3931

This theorem is referenced by: (None)