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Mirrors > Home > MPE Home > Th. List > wdomnumr | Structured version Visualization version Unicode version |
Description: Weak dominance agrees with normal for numerable right sets. (Contributed by Stefan O'Rear, 28-Feb-2015.) (Revised by Mario Carneiro, 5-May-2015.) |
Ref | Expression |
---|---|
wdomnumr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brwdom 8108 |
. . 3
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2 | 0domg 7725 |
. . . . 5
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3 | breq1 4419 |
. . . . 5
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4 | 2, 3 | syl5ibrcom 230 |
. . . 4
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5 | fodomnum 8514 |
. . . . 5
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6 | 5 | exlimdv 1790 |
. . . 4
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7 | 4, 6 | jaod 386 |
. . 3
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8 | 1, 7 | sylbid 223 |
. 2
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9 | domwdom 8115 |
. 2
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10 | 8, 9 | impbid1 208 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4529 ax-sep 4539 ax-nul 4548 ax-pow 4595 ax-pr 4653 ax-un 6610 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-reu 2756 df-rmo 2757 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-pss 3432 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4213 df-int 4249 df-iun 4294 df-br 4417 df-opab 4476 df-mpt 4477 df-tr 4512 df-eprel 4764 df-id 4768 df-po 4774 df-so 4775 df-fr 4812 df-se 4813 df-we 4814 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-rn 4864 df-res 4865 df-ima 4866 df-pred 5399 df-ord 5445 df-on 5446 df-suc 5448 df-iota 5565 df-fun 5603 df-fn 5604 df-f 5605 df-f1 5606 df-fo 5607 df-f1o 5608 df-fv 5609 df-isom 5610 df-riota 6277 df-ov 6318 df-oprab 6319 df-mpt2 6320 df-1st 6820 df-2nd 6821 df-wrecs 7054 df-recs 7116 df-er 7389 df-map 7500 df-en 7596 df-dom 7597 df-sdom 7598 df-wdom 8100 df-card 8399 df-acn 8402 |
This theorem is referenced by: wdomac 8981 ttac 35936 isnumbasgrplem2 36008 |
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