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Mirrors > Home > NFE Home > Th. List > dfiun2g | Unicode version |
Description: Alternate definition of indexed union when is a set. Definition 15(a) of [Suppes] p. 44. (Contributed by NM, 23-Mar-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
dfiun2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2664 | . . . . . 6 | |
2 | rsp 2674 | . . . . . . . 8 | |
3 | clel3g 2976 | . . . . . . . 8 | |
4 | 2, 3 | syl6 29 | . . . . . . 7 |
5 | 4 | imp 418 | . . . . . 6 |
6 | 1, 5 | rexbida 2629 | . . . . 5 |
7 | rexcom4 2878 | . . . . 5 | |
8 | 6, 7 | syl6bb 252 | . . . 4 |
9 | r19.41v 2764 | . . . . . 6 | |
10 | 9 | exbii 1582 | . . . . 5 |
11 | exancom 1586 | . . . . 5 | |
12 | 10, 11 | bitri 240 | . . . 4 |
13 | 8, 12 | syl6bb 252 | . . 3 |
14 | eliun 3973 | . . 3 | |
15 | eluniab 3903 | . . 3 | |
16 | 13, 14, 15 | 3bitr4g 279 | . 2 |
17 | 16 | eqrdv 2351 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 cab 2339 wral 2614 wrex 2615 cuni 3891 ciun 3969 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-v 2861 df-uni 3892 df-iun 3971 |
This theorem is referenced by: dfiun2 4001 uniqs 5984 |
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