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Mirrors > Home > MPE Home > Th. List > Mathboxes > 0cnALT3 | Structured version Visualization version GIF version |
Description: Alternate proof of 0cn 10822 using ax-resscn 10783, ax-addrcl 10787, ax-rnegex 10797, ax-cnre 10799 instead of ax-icn 10785, ax-addcl 10786, ax-mulcl 10788, ax-i2m1 10794. Version of 0cnALT 11063 using ax-1cn 10784 instead of ax-icn 10785. (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 10832 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | recni 10844 | 1 ⊢ 0 ∈ ℂ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2110 ℂcc 10724 0cc0 10726 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 ax-resscn 10783 ax-1cn 10784 ax-addrcl 10787 ax-rnegex 10797 ax-cnre 10799 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-ral 3063 df-rex 3064 df-v 3407 df-in 3870 df-ss 3880 |
This theorem is referenced by: (None) |
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