Theorem 0cnALT3 42271

Description: Alternate proof of 0cn 11232 using ax-resscn 11191, ax-addrcl 11195, ax-rnegex 11205, ax-cnre 11207 instead of ax-icn 11193, ax-addcl 11194, ax-mulcl 11196, ax-i2m1 11202. Version of 0cnALT 11475 using ax-1cn 11192 instead of ax-icn 11193. (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 11242	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11254	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2109  ℂcc 11132  0cc0 11134

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-resscn 11191  ax-1cn 11192  ax-addrcl 11195  ax-rnegex 11205  ax-cnre 11207

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2728  df-clel 2810  df-rex 3062  df-ss 3948

This theorem is referenced by: (None)