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Mirrors > Home > MPE Home > Th. List > smodm | Structured version Visualization version GIF version |
Description: The domain of a strictly monotone function is an ordinal. (Contributed by Andrew Salmon, 16-Nov-2011.) |
Ref | Expression |
---|---|
smodm | β’ (Smo π΄ β Ord dom π΄) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-smo 8293 | . 2 β’ (Smo π΄ β (π΄:dom π΄βΆOn β§ Ord dom π΄ β§ βπ₯ β dom π΄βπ¦ β dom π΄(π₯ β π¦ β (π΄βπ₯) β (π΄βπ¦)))) | |
2 | 1 | simp2bi 1147 | 1 β’ (Smo π΄ β Ord dom π΄) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β wcel 2107 βwral 3061 dom cdm 5634 Ord word 6317 Oncon0 6318 βΆwf 6493 βcfv 6497 Smo wsmo 8292 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 398 df-3an 1090 df-smo 8293 |
This theorem is referenced by: smores2 8301 smodm2 8302 smoel 8307 |
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