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Mirrors > Home > NFE Home > Th. List > unipr | Unicode version |
Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
unipr.1 | |
unipr.2 |
Ref | Expression |
---|---|
unipr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2863 | . . . . . . . 8 | |
2 | 1 | elpr 3752 | . . . . . . 7 |
3 | 2 | anbi2i 675 | . . . . . 6 |
4 | andi 837 | . . . . . 6 | |
5 | 3, 4 | bitri 240 | . . . . 5 |
6 | 5 | exbii 1582 | . . . 4 |
7 | 19.43 1605 | . . . 4 | |
8 | 6, 7 | bitri 240 | . . 3 |
9 | eluni 3895 | . . 3 | |
10 | elun 3221 | . . . 4 | |
11 | unipr.1 | . . . . . . 7 | |
12 | 11 | clel3 2978 | . . . . . 6 |
13 | exancom 1586 | . . . . . 6 | |
14 | 12, 13 | bitri 240 | . . . . 5 |
15 | unipr.2 | . . . . . . 7 | |
16 | 15 | clel3 2978 | . . . . . 6 |
17 | exancom 1586 | . . . . . 6 | |
18 | 16, 17 | bitri 240 | . . . . 5 |
19 | 14, 18 | orbi12i 507 | . . . 4 |
20 | 10, 19 | bitri 240 | . . 3 |
21 | 8, 9, 20 | 3bitr4i 268 | . 2 |
22 | 21 | eqriv 2350 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 357 wa 358 wex 1541 wceq 1642 wcel 1710 cvv 2860 cun 3208 cpr 3739 cuni 3892 |
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 2479 df-v 2862 df-nin 3212 df-compl 3213 df-un 3215 df-sn 3742 df-pr 3743 df-uni 3893 |
This theorem is referenced by: uniprg 3907 unisn 3908 uniintsn 3964 |
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