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Mirrors > Home > MPE Home > Th. List > 2cnALT | Structured version Visualization version GIF version |
Description: Alternate proof of 2cn 12286. Shorter but uses more axioms. Similar proofs are possible for 3cn 12292, ... , 9cn 12311. (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 12285 | . 2 ⊢ 2 ∈ ℝ | |
2 | 1 | recni 11227 | 1 ⊢ 2 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 ℂcc 11107 2c2 12266 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 ax-resscn 11166 ax-1cn 11167 ax-icn 11168 ax-addcl 11169 ax-addrcl 11170 ax-mulcl 11171 ax-mulrcl 11172 ax-i2m1 11177 ax-1ne0 11178 ax-rrecex 11181 ax-cnre 11182 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-iota 6495 df-fv 6551 df-ov 7411 df-2 12274 |
This theorem is referenced by: (None) |
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