Theorem 0cnALT3 42214

Description: Alternate proof of 0cn 11142 using ax-resscn 11101, ax-addrcl 11105, ax-rnegex 11115, ax-cnre 11117 instead of ax-icn 11103, ax-addcl 11104, ax-mulcl 11106, ax-i2m1 11112. Version of 0cnALT 11385 using ax-1cn 11102 instead of ax-icn 11103. (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 11152	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11164	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2109  ℂcc 11042  0cc0 11044

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 11101  ax-1cn 11102  ax-addrcl 11105  ax-rnegex 11115  ax-cnre 11117

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 3928

This theorem is referenced by: (None)