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Mirrors > Home > MPE Home > Th. List > relsdom | Structured version Visualization version Unicode version |
Description: Strict dominance is a relation. (Contributed by NM, 31-Mar-1998.) |
Ref | Expression |
---|---|
relsdom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reldom 7961 | . 2 | |
2 | reldif 5238 | . . 3 | |
3 | df-sdom 7958 | . . . 4 | |
4 | 3 | releqi 5202 | . . 3 |
5 | 2, 4 | sylibr 224 | . 2 |
6 | 1, 5 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cdif 3571 wrel 5119 cen 7952 cdom 7953 csdm 7954 |
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 |
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-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-opab 4713 df-xp 5120 df-rel 5121 df-dom 7957 df-sdom 7958 |
This theorem is referenced by: domdifsn 8043 sdom0 8092 sdomirr 8097 sdomdif 8108 sucdom2 8156 sdom1 8160 unxpdom 8167 unxpdom2 8168 sucxpdom 8169 isfinite2 8218 fin2inf 8223 card2on 8459 cdaxpdom 9011 cdafi 9012 cfslb2n 9090 isfin5 9121 isfin6 9122 isfin4-3 9137 fin56 9215 fin67 9217 sdomsdomcard 9382 gchi 9446 canthp1lem1 9474 canthp1lem2 9475 canthp1 9476 frgpnabl 18278 fphpd 37380 |
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