Theorem 0cnALT3 43570

Description: Alternate proof of 0cn 11337 using ax-resscn 11296, ax-addrcl 11300, ax-rnegex 11310, ax-cnre 11312 instead of ax-icn 11298, ax-addcl 11299, ax-mulcl 11301, ax-i2m1 11307. Version of 0cnALT 11584 using ax-1cn 11297 instead of ax-icn 11298. (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 11349	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11362	1 ⊢ 0 ∈ ℂ

This proof depends on syntax axioms:   ∈ wcel 2147  ℂcc 11237  0cc0 11239

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-resscn 11296  ax-1cn 11297  ax-addrcl 11300  ax-rnegex 11310  ax-cnre 11312

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2755  df-clel 2839  df-rex 3091  df-ss 3901

This theorem is used by: (None)