Theorem 0cnALT3 42450

Description: Alternate proof of 0cn 11122 using ax-resscn 11081, ax-addrcl 11085, ax-rnegex 11095, ax-cnre 11097 instead of ax-icn 11083, ax-addcl 11084, ax-mulcl 11086, ax-i2m1 11092. Version of 0cnALT 11366 using ax-1cn 11082 instead of ax-icn 11083. (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 11132	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11144	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2113  ℂcc 11022  0cc0 11024

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-resscn 11081  ax-1cn 11082  ax-addrcl 11085  ax-rnegex 11095  ax-cnre 11097

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-cleq 2726  df-clel 2809  df-rex 3059  df-ss 3916

This theorem is referenced by: (None)