| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > eusv2nf | Unicode version | ||
| Description: Two ways to express
single-valuedness of a class expression
|
| Ref | Expression |
|---|---|
| eusv2.1 |
|
| Ref | Expression |
|---|---|
| eusv2nf |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfeu1 2056 |
. . . 4
| |
| 2 | nfe1 1510 |
. . . . . . 7
| |
| 3 | 2 | nfeu 2064 |
. . . . . 6
|
| 4 | eusv2.1 |
. . . . . . . . 9
| |
| 5 | 4 | isseti 2771 |
. . . . . . . 8
|
| 6 | 19.8a 1604 |
. . . . . . . . 9
| |
| 7 | 6 | ancri 324 |
. . . . . . . 8
|
| 8 | 5, 7 | eximii 1616 |
. . . . . . 7
|
| 9 | eupick 2124 |
. . . . . . 7
| |
| 10 | 8, 9 | mpan2 425 |
. . . . . 6
|
| 11 | 3, 10 | alrimi 1536 |
. . . . 5
|
| 12 | nf3 1683 |
. . . . 5
| |
| 13 | 11, 12 | sylibr 134 |
. . . 4
|
| 14 | 1, 13 | alrimi 1536 |
. . 3
|
| 15 | dfnfc2 3857 |
. . . 4
| |
| 16 | 15, 4 | mpg 1465 |
. . 3
|
| 17 | 14, 16 | sylibr 134 |
. 2
|
| 18 | eusvnfb 4489 |
. . . 4
| |
| 19 | 4, 18 | mpbiran2 943 |
. . 3
|
| 20 | eusv2i 4490 |
. . 3
| |
| 21 | 19, 20 | sylbir 135 |
. 2
|
| 22 | 17, 21 | impbii 126 |
1
|
| 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 710 ax-5 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-10 1519 ax-11 1520 ax-i12 1521 ax-bndl 1523 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 ax-ext 2178 |
| This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1475 df-sb 1777 df-eu 2048 df-mo 2049 df-clab 2183 df-cleq 2189 df-clel 2192 df-nfc 2328 df-rex 2481 df-v 2765 df-sbc 2990 df-csb 3085 df-un 3161 df-sn 3628 df-pr 3629 df-uni 3840 |
| This theorem is referenced by: eusv2 4492 |
| Copyright terms: Public domain | W3C validator |