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Mirrors > Home > MPE Home > Th. List > 2cnALT | Structured version Visualization version GIF version |
Description: Alternate proof of 2cn 12236. Shorter but uses more axioms. Similar proofs are possible for 3cn 12242, ... , 9cn 12261. (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 12235 | . 2 ⊢ 2 ∈ ℝ | |
2 | 1 | recni 11177 | 1 ⊢ 2 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 ℂcc 11057 2c2 12216 |
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 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 ax-resscn 11116 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-addrcl 11120 ax-mulcl 11121 ax-mulrcl 11122 ax-i2m1 11127 ax-1ne0 11128 ax-rrecex 11131 ax-cnre 11132 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-iota 6452 df-fv 6508 df-ov 7364 df-2 12224 |
This theorem is referenced by: (None) |
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