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Mirrors > Home > ILE Home > Th. List > issmo2 | Unicode version |
Description: Alternative definition of a strictly monotone ordinal function. (Contributed by Mario Carneiro, 12-Mar-2013.) |
Ref | Expression |
---|---|
issmo2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fss 5054 | . . . . 5 | |
2 | 1 | ex 108 | . . . 4 |
3 | fdm 5050 | . . . . 5 | |
4 | 3 | feq2d 5035 | . . . 4 |
5 | 2, 4 | sylibrd 158 | . . 3 |
6 | ordeq 4109 | . . . . 5 | |
7 | 3, 6 | syl 14 | . . . 4 |
8 | 7 | biimprd 147 | . . 3 |
9 | 3 | raleqdv 2511 | . . . 4 |
10 | 9 | biimprd 147 | . . 3 |
11 | 5, 8, 10 | 3anim123d 1214 | . 2 |
12 | dfsmo2 5902 | . 2 | |
13 | 11, 12 | syl6ibr 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wceq 1243 wcel 1393 wral 2306 wss 2917 word 4099 con0 4100 cdm 4345 wf 4898 cfv 4902 wsmo 5900 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-in 2924 df-ss 2931 df-uni 3581 df-tr 3855 df-iord 4103 df-fn 4905 df-f 4906 df-smo 5901 |
This theorem is referenced by: (None) |
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