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Mirrors > Home > NFE Home > Th. List > disj3 | Unicode version |
Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.) |
Ref | Expression |
---|---|
disj3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71 611 | . . . 4 | |
2 | eldif 3221 | . . . . 5 | |
3 | 2 | bibi2i 304 | . . . 4 |
4 | 1, 3 | bitr4i 243 | . . 3 |
5 | 4 | albii 1566 | . 2 |
6 | disj1 3593 | . 2 | |
7 | dfcleq 2347 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wal 1540 wceq 1642 wcel 1710 cdif 3206 cin 3208 c0 3550 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-nul 3551 |
This theorem is referenced by: disjel 3597 disj4 3599 uneqdifeq 3638 difprsn1 3847 diftpsn3 3849 ssunsn2 3865 |
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