Theorem 0cnALT3 43041

Description: Alternate proof of 0cn 11193 using ax-resscn 11152, ax-addrcl 11156, ax-rnegex 11166, ax-cnre 11168 instead of ax-icn 11154, ax-addcl 11155, ax-mulcl 11157, ax-i2m1 11163. Version of 0cnALT 11440 using ax-1cn 11153 instead of ax-icn 11154. (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 11205	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11218	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2143  ℂcc 11093  0cc0 11095

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-resscn 11152  ax-1cn 11153  ax-addrcl 11156  ax-rnegex 11166  ax-cnre 11168

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810  df-cleq 2755  df-clel 2838  df-rex 3090  df-ss 3922

This theorem is referenced by: (None)