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Mirrors > Home > MPE Home > Th. List > endom | Structured version Visualization version Unicode version |
Description: Equinumerosity implies dominance. Theorem 15 of [Suppes] p. 94. (Contributed by NM, 28-May-1998.) |
Ref | Expression |
---|---|
endom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | enssdom 7980 | . 2 | |
2 | 1 | ssbri 4697 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 class class class wbr 4653 cen 7952 cdom 7953 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-f1o 5895 df-en 7956 df-dom 7957 |
This theorem is referenced by: bren2 7986 domrefg 7990 endomtr 8014 domentr 8015 domunsncan 8060 sbthb 8081 sdomentr 8094 ensdomtr 8096 domtriord 8106 domunsn 8110 xpen 8123 unxpdom2 8168 sucxpdom 8169 wdomen1 8481 wdomen2 8482 fidomtri2 8820 prdom2 8829 acnen 8876 acnen2 8878 alephdom 8904 alephinit 8918 uncdadom 8993 pwcdadom 9038 fin1a2lem11 9232 hsmexlem1 9248 gchdomtri 9451 gchcdaidm 9490 gchxpidm 9491 gchpwdom 9492 gchhar 9501 gruina 9640 nnct 12780 odinf 17980 hauspwdom 21304 ufildom1 21730 iscmet3 23091 ovolctb2 23260 mbfaddlem 23427 heiborlem3 33612 zct 39229 qct 39578 caratheodory 40742 |
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