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Mirrors > Home > ILE Home > Th. List > apsscn | Unicode version |
Description: The points apart from a given point are complex numbers. (Contributed by Jim Kingdon, 19-Dec-2023.) |
Ref | Expression |
---|---|
apsscn | # |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 3980 | . . . . 5 # # | |
2 | 1 | elrab 2878 | . . . 4 # # |
3 | aprcl 8536 | . . . 4 # | |
4 | 2, 3 | simplbiim 385 | . . 3 # |
5 | 4 | simpld 111 | . 2 # |
6 | 5 | ssriv 3142 | 1 # |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 2135 crab 2446 wss 3112 class class class wbr 3977 cc 7743 # cap 8471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 ax-un 4406 ax-resscn 7837 ax-icn 7840 ax-addcl 7841 ax-mulcl 7843 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-sbc 2948 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-mpt 4040 df-id 4266 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-rn 4610 df-iota 5148 df-fun 5185 df-fn 5186 df-f 5187 df-fo 5189 df-fv 5191 df-1st 6101 df-2nd 6102 df-ap 8472 |
This theorem is referenced by: limccoap 13214 dveflem 13254 |
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