Theorem 0cnALT3 42623

Description: Alternate proof of 0cn 11136 using ax-resscn 11095, ax-addrcl 11099, ax-rnegex 11109, ax-cnre 11111 instead of ax-icn 11097, ax-addcl 11098, ax-mulcl 11100, ax-i2m1 11106. Version of 0cnALT 11380 using ax-1cn 11096 instead of ax-icn 11097. (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 11146	. 2 ⊢ 0 ∈ ℝ
2	1	recni 11158	1 ⊢ 0 ∈ ℂ

Syntax hints:   ∈ wcel 2114  ℂcc 11036  0cc0 11038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-resscn 11095  ax-1cn 11096  ax-addrcl 11099  ax-rnegex 11109  ax-cnre 11111

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729  df-clel 2812  df-rex 3063  df-ss 3920

This theorem is referenced by: (None)