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Mirrors > Home > MPE Home > Th. List > ustneism | Structured version Visualization version Unicode version |
Description: For a point ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ustneism |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snnzg 4101 |
. . . 4
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2 | 1 | adantl 472 |
. . 3
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3 | xpco 5394 |
. . 3
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4 | 2, 3 | syl 17 |
. 2
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5 | cnvxp 5272 |
. . . . 5
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6 | ressn 5390 |
. . . . . . 7
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7 | 6 | cnveqi 5027 |
. . . . . 6
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8 | resss 5146 |
. . . . . . 7
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9 | cnvss 5025 |
. . . . . . 7
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10 | 8, 9 | ax-mp 5 |
. . . . . 6
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11 | 7, 10 | eqsstr3i 3474 |
. . . . 5
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12 | 5, 11 | eqsstr3i 3474 |
. . . 4
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13 | coss2 5009 |
. . . 4
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14 | 12, 13 | mp1i 13 |
. . 3
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15 | 6, 8 | eqsstr3i 3474 |
. . . 4
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16 | coss1 5008 |
. . . 4
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17 | 15, 16 | mp1i 13 |
. . 3
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18 | 14, 17 | sstrd 3453 |
. 2
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19 | 4, 18 | eqsstr3d 3478 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-sbc 3279 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-br 4416 df-opab 4475 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 |
This theorem is referenced by: neipcfilu 21359 |
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