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Mirrors > Home > MPE Home > Th. List > brdomi | Structured version Visualization version Unicode version |
Description: Dominance relation. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
brdomi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reldom 7961 | . . . 4 | |
2 | 1 | brrelex2i 5159 | . . 3 |
3 | brdomg 7965 | . . 3 | |
4 | 2, 3 | syl 17 | . 2 |
5 | 4 | ibi 256 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wex 1704 wcel 1990 cvv 3200 class class class wbr 4653 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-8 1992 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 ax-un 6949 |
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-ral 2917 df-rex 2918 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-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-cnv 5122 df-dm 5124 df-rn 5125 df-fn 5891 df-f 5892 df-f1 5893 df-dom 7957 |
This theorem is referenced by: ctex 7970 2dom 8029 xpdom2 8055 domunsncan 8060 fodomr 8111 domssex 8121 sucdom2 8156 hartogslem1 8447 infdifsn 8554 acndom 8874 acndom2 8877 fictb 9067 fin23lem41 9174 iundom2g 9362 pwfseq 9486 omssubadd 30362 |
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