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Mirrors > Home > ILE Home > Th. List > issmo2 | Unicode version |
Description: Alternate definition of a strictly monotone ordinal function. (Contributed by Mario Carneiro, 12-Mar-2013.) |
Ref | Expression |
---|---|
issmo2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fss 5284 | . . . . 5 | |
2 | 1 | ex 114 | . . . 4 |
3 | fdm 5278 | . . . . 5 | |
4 | 3 | feq2d 5260 | . . . 4 |
5 | 2, 4 | sylibrd 168 | . . 3 |
6 | ordeq 4294 | . . . . 5 | |
7 | 3, 6 | syl 14 | . . . 4 |
8 | 7 | biimprd 157 | . . 3 |
9 | 3 | raleqdv 2632 | . . . 4 |
10 | 9 | biimprd 157 | . . 3 |
11 | 5, 8, 10 | 3anim123d 1297 | . 2 |
12 | dfsmo2 6184 | . 2 | |
13 | 11, 12 | syl6ibr 161 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wceq 1331 wcel 1480 wral 2416 wss 3071 word 4284 con0 4285 cdm 4539 wf 5119 cfv 5123 wsmo 6182 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 df-tr 4027 df-iord 4288 df-fn 5126 df-f 5127 df-smo 6183 |
This theorem is referenced by: (None) |
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