Theorem 0cnALT3 42248

Description: Alternate proof of 0cn 11282 using ax-resscn 11241, ax-addrcl 11245, ax-rnegex 11255, ax-cnre 11257 instead of ax-icn 11243, ax-addcl 11244, ax-mulcl 11246, ax-i2m1 11252. Version of 0cnALT 11524 using ax-1cn 11242 instead of ax-icn 11243. (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 11292	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11304	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2108  ℂcc 11182  0cc0 11184

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-resscn 11241  ax-1cn 11242  ax-addrcl 11245  ax-rnegex 11255  ax-cnre 11257

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-cleq 2732  df-clel 2819  df-rex 3077  df-ss 3993

This theorem is referenced by: (None)