Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > reldom | Structured version Visualization version Unicode version |
Description: Dominance is a relation. (Contributed by NM, 28-Mar-1998.) |
Ref | Expression |
---|---|
reldom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dom 7957 | . 2 | |
2 | 1 | relopabi 5245 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wex 1704 wrel 5119 wf1 5885 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 |
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 |
This theorem is referenced by: relsdom 7962 brdomg 7965 brdomi 7966 domtr 8009 undom 8048 xpdom2 8055 xpdom1g 8057 domunsncan 8060 sbth 8080 sbthcl 8082 dom0 8088 fodomr 8111 pwdom 8112 domssex 8121 mapdom1 8125 mapdom2 8131 fineqv 8175 infsdomnn 8221 infn0 8222 elharval 8468 harword 8470 domwdom 8479 unxpwdom 8494 infdifsn 8554 infdiffi 8555 ac10ct 8857 iunfictbso 8937 cdadom1 9008 cdainf 9014 infcda1 9015 pwcdaidm 9017 cdalepw 9018 unctb 9027 infcdaabs 9028 infunabs 9029 infpss 9039 infmap2 9040 fictb 9067 infpssALT 9135 fin34 9212 ttukeylem1 9331 fodomb 9348 wdomac 9349 brdom3 9350 iundom2g 9362 iundom 9364 infxpidm 9384 iunctb 9396 gchdomtri 9451 pwfseq 9486 pwxpndom2 9487 pwxpndom 9488 pwcdandom 9489 gchpwdom 9492 gchaclem 9500 reexALT 11826 hashdomi 13169 1stcrestlem 21255 2ndcdisj2 21260 dis2ndc 21263 hauspwdom 21304 ufilen 21734 ovoliunnul 23275 uniiccdif 23346 ovoliunnfl 33451 voliunnfl 33453 volsupnfl 33454 nnfoctb 39213 meadjiun 40683 caragenunicl 40738 |
Copyright terms: Public domain | W3C validator |