Theorem 0cnALT3 43304

Description: Alternate proof of 0cn 11298 using ax-resscn 11257, ax-addrcl 11261, ax-rnegex 11271, ax-cnre 11273 instead of ax-icn 11259, ax-addcl 11260, ax-mulcl 11262, ax-i2m1 11268. Version of 0cnALT 11545 using ax-1cn 11258 instead of ax-icn 11259. (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 11310	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11323	1 ⊢ 0 ∈ ℂ

This proof depends on syntax axioms:   ∈ wcel 2145  ℂcc 11198  0cc0 11200

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 2733  ax-resscn 11257  ax-1cn 11258  ax-addrcl 11261  ax-rnegex 11271  ax-cnre 11273

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2753  df-clel 2836  df-rex 3088  df-ss 3916

This theorem is used by: (None)