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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 2056 |
. 2
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2 | vex 2740 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
3 | nfcv 2319 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
4 | nfcsb1v 3090 |
. . . . . . . . 9
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5 | 4 | nfeq2 2331 |
. . . . . . . 8
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6 | csbeq1a 3066 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | eqeq2d 2189 |
. . . . . . . 8
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8 | 3, 5, 7 | spcgf 2819 |
. . . . . . 7
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9 | 2, 8 | ax-mp 5 |
. . . . . 6
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10 | vex 2740 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
11 | nfcv 2319 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
12 | nfcsb1v 3090 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 12 | nfeq2 2331 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | csbeq1a 3066 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | eqeq2d 2189 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 11, 13, 15 | spcgf 2819 |
. . . . . . 7
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17 | 10, 16 | ax-mp 5 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 9, 17 | eqtr3d 2212 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 18 | alrimivv 1875 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | sbnfc2 3117 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | sylibr 134 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | exlimiv 1598 |
. 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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sbc 2963 df-csb 3058 |
This theorem is referenced by: eusvnfb 4451 eusv2i 4452 |
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