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Mirrors > Home > MPE Home > Th. List > ustinvel | Structured version Visualization version Unicode version |
Description: If ![]() |
Ref | Expression |
---|---|
ustinvel |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfvex 5897 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | isust 21230 |
. . . . . . 7
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3 | 1, 2 | syl 17 |
. . . . . 6
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4 | 3 | ibi 245 |
. . . . 5
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5 | 4 | simp3d 1023 |
. . . 4
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6 | sseq1 3455 |
. . . . . . . 8
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7 | 6 | imbi1d 319 |
. . . . . . 7
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8 | 7 | ralbidv 2829 |
. . . . . 6
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9 | ineq1 3629 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | eleq1d 2515 |
. . . . . . 7
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11 | 10 | ralbidv 2829 |
. . . . . 6
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12 | sseq2 3456 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | cnveq 5011 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 13 | eleq1d 2515 |
. . . . . . 7
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15 | sseq2 3456 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | rexbidv 2903 |
. . . . . . 7
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17 | 12, 14, 16 | 3anbi123d 1341 |
. . . . . 6
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18 | 8, 11, 17 | 3anbi123d 1341 |
. . . . 5
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19 | 18 | rspcv 3148 |
. . . 4
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20 | 5, 19 | mpan9 472 |
. . 3
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21 | 20 | simp3d 1023 |
. 2
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22 | 21 | simp2d 1022 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-sbc 3270 df-csb 3366 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-pw 3955 df-sn 3971 df-pr 3973 df-op 3977 df-uni 4202 df-br 4406 df-opab 4465 df-mpt 4466 df-id 4752 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-res 4849 df-iota 5549 df-fun 5587 df-fv 5593 df-ust 21227 |
This theorem is referenced by: ustexsym 21242 trust 21256 |
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