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Mirrors > Home > MPE Home > Th. List > Mathboxes > 0cnALT3 | Structured version Visualization version GIF version |
Description: Alternate proof of 0cn 11207 using ax-resscn 11166, ax-addrcl 11170, ax-rnegex 11180, ax-cnre 11182 instead of ax-icn 11168, ax-addcl 11169, ax-mulcl 11171, ax-i2m1 11177. Version of 0cnALT 11449 using ax-1cn 11167 instead of ax-icn 11168. (Contributed by Steven Nguyen, 7-Jan-2022.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
0cnALT3 | ⊢ 0 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 11217 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | recni 11229 | 1 ⊢ 0 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2098 ℂcc 11107 0cc0 11109 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 ax-resscn 11166 ax-1cn 11167 ax-addrcl 11170 ax-rnegex 11180 ax-cnre 11182 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-rex 3065 df-v 3470 df-in 3950 df-ss 3960 |
This theorem is referenced by: (None) |
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