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Mirrors > Home > MPE Home > Th. List > Mathboxes > 0cnALT3 | Structured version Visualization version GIF version |
Description: Alternate proof of 0cn 10368 using ax-resscn 10329, ax-addrcl 10333, ax-rnegex 10343, ax-cnre 10345 instead of ax-icn 10331, ax-addcl 10332, ax-mulcl 10334, ax-i2m1 10340. Version of 0cnALT 10610 using ax-1cn 10330 instead of ax-icn 10331. (Contributed by Steven Nguyen, 7-Jan-2022.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
0cnALT3 | ⊢ 0 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 10378 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | recni 10391 | 1 ⊢ 0 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 ℂcc 10270 0cc0 10272 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-ext 2754 ax-resscn 10329 ax-1cn 10330 ax-addrcl 10333 ax-rnegex 10343 ax-cnre 10345 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-ral 3095 df-rex 3096 df-in 3799 df-ss 3806 |
This theorem is referenced by: (None) |
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