Theorem 0cnALT3 43081

Description: Alternate proof of 0cn 11215 using ax-resscn 11174, ax-addrcl 11178, ax-rnegex 11188, ax-cnre 11190 instead of ax-icn 11176, ax-addcl 11177, ax-mulcl 11179, ax-i2m1 11185. Version of 0cnALT 11462 using ax-1cn 11175 instead of ax-icn 11176. (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 11227	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11240	1 ⊢ 0 ∈ ℂ

This proof depends on syntax axioms:   ∈ wcel 2146  ℂcc 11115  0cc0 11117

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-resscn 11174  ax-1cn 11175  ax-addrcl 11178  ax-rnegex 11188  ax-cnre 11190

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2757  df-clel 2840  df-rex 3092  df-ss 3923

This theorem is used by: (None)