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Mirrors > Home > ILE Home > Th. List > eusvnf | Unicode version |
Description: Even if ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eusvnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2030 |
. 2
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2 | vex 2692 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
3 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
4 | nfcsb1v 3040 |
. . . . . . . . 9
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5 | 4 | nfeq2 2294 |
. . . . . . . 8
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6 | csbeq1a 3016 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | eqeq2d 2152 |
. . . . . . . 8
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8 | 3, 5, 7 | spcgf 2771 |
. . . . . . 7
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9 | 2, 8 | ax-mp 5 |
. . . . . 6
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10 | vex 2692 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
11 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
12 | nfcsb1v 3040 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 12 | nfeq2 2294 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | csbeq1a 3016 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | eqeq2d 2152 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 11, 13, 15 | spcgf 2771 |
. . . . . . 7
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17 | 10, 16 | ax-mp 5 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 9, 17 | eqtr3d 2175 |
. . . . 5
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19 | 18 | alrimivv 1848 |
. . . 4
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20 | sbnfc2 3065 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | sylibr 133 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | exlimiv 1578 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 22 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-sbc 2914 df-csb 3008 |
This theorem is referenced by: eusvnfb 4383 eusv2i 4384 |
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