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Mirrors > Home > MPE Home > Th. List > 2cnALT | Structured version Visualization version GIF version |
Description: Alternate proof of 2cn 12339. Shorter but uses more axioms. Similar proofs are possible for 3cn 12345, ... , 9cn 12364. (Contributed by NM, 30-Jul-2004.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
2cnALT | ⊢ 2 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2re 12338 | . 2 ⊢ 2 ∈ ℝ | |
2 | 1 | recni 11278 | 1 ⊢ 2 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2099 ℂcc 11156 2c2 12319 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 ax-resscn 11215 ax-1cn 11216 ax-icn 11217 ax-addcl 11218 ax-addrcl 11219 ax-mulcl 11220 ax-mulrcl 11221 ax-i2m1 11226 ax-1ne0 11227 ax-rrecex 11230 ax-cnre 11231 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-ne 2931 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3464 df-dif 3950 df-un 3952 df-ss 3964 df-nul 4326 df-if 4534 df-sn 4634 df-pr 4636 df-op 4640 df-uni 4914 df-br 5154 df-iota 6506 df-fv 6562 df-ov 7427 df-2 12327 |
This theorem is referenced by: (None) |
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