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Mirrors > Home > MPE Home > Th. List > Mathboxes > 0cnALT3 | Structured version Visualization version GIF version |
Description: Alternate proof of 0cn 10627 using ax-resscn 10588, ax-addrcl 10592, ax-rnegex 10602, ax-cnre 10604 instead of ax-icn 10590, ax-addcl 10591, ax-mulcl 10593, ax-i2m1 10599. Version of 0cnALT 10868 using ax-1cn 10589 instead of ax-icn 10590. (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 10637 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | recni 10649 | 1 ⊢ 0 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2110 ℂcc 10529 0cc0 10531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2156 ax-12 2172 ax-ext 2793 ax-resscn 10588 ax-1cn 10589 ax-addrcl 10592 ax-rnegex 10602 ax-cnre 10604 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-ral 3143 df-rex 3144 df-in 3943 df-ss 3952 |
This theorem is referenced by: (None) |
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