| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > ordsucss | Unicode version | ||
| Description: The successor of an element of an ordinal class is a subset of it. (Contributed by NM, 21-Jun-1998.) |
| Ref | Expression |
|---|---|
| ordsucss |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ordtr 4424 |
. 2
| |
| 2 | trss 4150 |
. . . . 5
| |
| 3 | snssi 3776 |
. . . . . 6
| |
| 4 | 3 | a1i 9 |
. . . . 5
|
| 5 | 2, 4 | jcad 307 |
. . . 4
|
| 6 | unss 3346 |
. . . 4
| |
| 7 | 5, 6 | imbitrdi 161 |
. . 3
|
| 8 | df-suc 4417 |
. . . 4
| |
| 9 | 8 | sseq1i 3218 |
. . 3
|
| 10 | 7, 9 | imbitrrdi 162 |
. 2
|
| 11 | 1, 10 | syl 14 |
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 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-v 2773 df-un 3169 df-in 3171 df-ss 3178 df-sn 3638 df-uni 3850 df-tr 4142 df-iord 4412 df-suc 4417 |
| This theorem is referenced by: ordelsuc 4552 tfrlemibfn 6413 tfr1onlembfn 6429 tfrcllembfn 6442 sucinc2 6531 nndomo 6960 prarloclemn 7611 ennnfonelemhom 12757 ennnfonelemrn 12761 |
| Copyright terms: Public domain | W3C validator |