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Mirrors > Home > MPE Home > Th. List > disj3 | Structured version Unicode version |
Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.) |
Ref | Expression |
---|---|
disj3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71 630 |
. . . 4
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2 | eldif 3449 |
. . . . 5
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3 | 2 | bibi2i 313 |
. . . 4
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4 | 1, 3 | bitr4i 252 |
. . 3
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5 | 4 | albii 1611 |
. 2
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6 | disj1 3832 |
. 2
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7 | dfcleq 2447 |
. 2
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8 | 5, 6, 7 | 3bitr4i 277 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-v 3080 df-dif 3442 df-in 3446 df-nul 3749 |
This theorem is referenced by: disjel 3836 disj4 3838 uneqdifeq 3878 difprsn1 4121 diftpsn3 4123 ssunsn2 4143 orddif 4923 php 7608 hartogslem1 7870 infeq5i 7956 cantnfp1lem3 8002 cantnfp1lem3OLD 8028 cda1dif 8459 infcda1 8476 ssxr 9558 dprd2da 16666 dmdprdsplit2lem 16669 ablfac1eulem 16698 lbsextlem4 17368 opsrtoslem2 17693 alexsublem 19751 volun 21162 lhop1lem 21621 ex-dif 23802 difeq 26071 imadifxp 26110 disjdsct 26169 probun 26966 ballotlemfp1 27038 finixpnum 28582 asindmre 28647 kelac2 29586 pwfi2f1o 29619 |
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