Theorem 0cnALT3 43444

Description: Alternate proof of 0cn 11308 using ax-resscn 11267, ax-addrcl 11271, ax-rnegex 11281, ax-cnre 11283 instead of ax-icn 11269, ax-addcl 11270, ax-mulcl 11272, ax-i2m1 11278. Version of 0cnALT 11555 using ax-1cn 11268 instead of ax-icn 11269. (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 11320	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11333	1 ⊢ 0 ∈ ℂ

This proof depends on syntax axioms:   ∈ wcel 2146  ℂcc 11208  0cc0 11210

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-resscn 11267  ax-1cn 11268  ax-addrcl 11271  ax-rnegex 11281  ax-cnre 11283

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-cleq 2755  df-clel 2838  df-rex 3090  df-ss 3900

This theorem is used by: (None)