Theorem 0cnALT3 43121

Description: Alternate proof of 0cn 11223 using ax-resscn 11182, ax-addrcl 11186, ax-rnegex 11196, ax-cnre 11198 instead of ax-icn 11184, ax-addcl 11185, ax-mulcl 11187, ax-i2m1 11193. Version of 0cnALT 11470 using ax-1cn 11183 instead of ax-icn 11184. (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 11235	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11248	1 ⊢ 0 ∈ ℂ

This proof depends on syntax axioms:   ∈ wcel 2145  ℂcc 11123  0cc0 11125

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 2147  ax-9 2155  ax-ext 2732  ax-resscn 11182  ax-1cn 11183  ax-addrcl 11186  ax-rnegex 11196  ax-cnre 11198

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2752  df-clel 2835  df-rex 3087  df-ss 3916

This theorem is used by: (None)