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Mirrors > Home > MPE Home > Th. List > 2cnALT | Structured version Visualization version GIF version |
Description: Alternate proof of 2cn 12048. Shorter but uses more axioms. Similar proofs are possible for 3cn 12054, ... , 9cn 12073. (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 12047 | . 2 ⊢ 2 ∈ ℝ | |
2 | 1 | recni 10989 | 1 ⊢ 2 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 ℂcc 10869 2c2 12028 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 ax-resscn 10928 ax-1cn 10929 ax-icn 10930 ax-addcl 10931 ax-addrcl 10932 ax-mulcl 10933 ax-mulrcl 10934 ax-i2m1 10939 ax-1ne0 10940 ax-rrecex 10943 ax-cnre 10944 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-ne 2944 df-ral 3069 df-rex 3070 df-rab 3073 df-v 3434 df-dif 3890 df-un 3892 df-in 3894 df-ss 3904 df-nul 4257 df-if 4460 df-sn 4562 df-pr 4564 df-op 4568 df-uni 4840 df-br 5075 df-iota 6391 df-fv 6441 df-ov 7278 df-2 12036 |
This theorem is referenced by: (None) |
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