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Mirrors > Home > MPE Home > Th. List > 2cnALT | Structured version Visualization version GIF version |
Description: Alternate proof of 2cn 11791. Shorter but uses more axioms. Similar proofs are possible for 3cn 11797, ... , 9cn 11816. (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 11790 | . 2 ⊢ 2 ∈ ℝ | |
2 | 1 | recni 10733 | 1 ⊢ 2 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 ℂcc 10613 2c2 11771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2710 ax-resscn 10672 ax-1cn 10673 ax-icn 10674 ax-addcl 10675 ax-addrcl 10676 ax-mulcl 10677 ax-mulrcl 10678 ax-i2m1 10683 ax-1ne0 10684 ax-rrecex 10687 ax-cnre 10688 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-ne 2935 df-ral 3058 df-rex 3059 df-v 3400 df-un 3848 df-in 3850 df-ss 3860 df-sn 4517 df-pr 4519 df-op 4523 df-uni 4797 df-br 5031 df-iota 6297 df-fv 6347 df-ov 7173 df-2 11779 |
This theorem is referenced by: (None) |
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