| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > hashinfuni | Unicode version | ||
| Description: The ordinal size of an
infinite set is |
| Ref | Expression |
|---|---|
| hashinfuni |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | omex 4641 |
. . . . . 6
| |
| 2 | 1 | snid 3664 |
. . . . 5
|
| 3 | elun2 3341 |
. . . . 5
| |
| 4 | breq1 4047 |
. . . . . 6
| |
| 5 | 4 | elrab3 2930 |
. . . . 5
|
| 6 | 2, 3, 5 | mp2b 8 |
. . . 4
|
| 7 | 6 | biimpri 133 |
. . 3
|
| 8 | elrabi 2926 |
. . . . . . 7
| |
| 9 | elun 3314 |
. . . . . . 7
| |
| 10 | 8, 9 | sylib 122 |
. . . . . 6
|
| 11 | ordom 4655 |
. . . . . . . 8
| |
| 12 | ordelss 4426 |
. . . . . . . 8
| |
| 13 | 11, 12 | mpan 424 |
. . . . . . 7
|
| 14 | elsni 3651 |
. . . . . . . 8
| |
| 15 | eqimss 3247 |
. . . . . . . 8
| |
| 16 | 14, 15 | syl 14 |
. . . . . . 7
|
| 17 | 13, 16 | jaoi 718 |
. . . . . 6
|
| 18 | 10, 17 | syl 14 |
. . . . 5
|
| 19 | 18 | adantl 277 |
. . . 4
|
| 20 | 19 | ralrimiva 2579 |
. . 3
|
| 21 | ssunieq 3883 |
. . 3
| |
| 22 | 7, 20, 21 | syl2anc 411 |
. 2
|
| 23 | 22 | eqcomd 2211 |
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-in1 615 ax-in2 616 ax-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-nul 4170 ax-pow 4218 ax-pr 4253 ax-un 4480 ax-iinf 4636 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-rab 2493 df-v 2774 df-dif 3168 df-un 3170 df-in 3172 df-ss 3179 df-nul 3461 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-int 3886 df-br 4045 df-tr 4143 df-iord 4413 df-suc 4418 df-iom 4639 |
| This theorem is referenced by: hashinfom 10923 |
| Copyright terms: Public domain | W3C validator |