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Mirrors > Home > MPE Home > Th. List > eusvnf | Unicode version |
Description: Even if ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eusvnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2281 |
. 2
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2 | vex 2923 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
3 | nfcv 2544 |
. . . . . . . 8
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4 | nfcsb1v 3247 |
. . . . . . . . 9
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5 | 4 | nfeq2 2555 |
. . . . . . . 8
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6 | csbeq1a 3223 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | eqeq2d 2419 |
. . . . . . . 8
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8 | 3, 5, 7 | spcgf 2995 |
. . . . . . 7
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9 | 2, 8 | ax-mp 8 |
. . . . . 6
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10 | vex 2923 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
11 | nfcv 2544 |
. . . . . . . 8
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12 | nfcsb1v 3247 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 12 | nfeq2 2555 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | csbeq1a 3223 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | eqeq2d 2419 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 11, 13, 15 | spcgf 2995 |
. . . . . . 7
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17 | 10, 16 | ax-mp 8 |
. . . . . 6
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18 | 9, 17 | eqtr3d 2442 |
. . . . 5
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19 | 18 | alrimivv 1639 |
. . . 4
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20 | sbnfc2 3273 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | sylibr 204 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | exlimiv 1641 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 22 | syl 16 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: eusvnfb 4682 eusv2i 4683 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 |
This theorem depends on definitions: df-bi 178 df-an 361 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2262 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-v 2922 df-sbc 3126 df-csb 3216 |
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