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Mirrors > Home > ILE Home > Th. List > iunxpf | Unicode version |
Description: Indexed union on a cross product is equals a double indexed union. The hypothesis specifies an implicit substitution. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
iunxpf.1 | |
iunxpf.2 | |
iunxpf.3 | |
iunxpf.4 |
Ref | Expression |
---|---|
iunxpf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxpf.1 | . . . . 5 | |
2 | 1 | nfcri 2273 | . . . 4 |
3 | iunxpf.2 | . . . . 5 | |
4 | 3 | nfcri 2273 | . . . 4 |
5 | iunxpf.3 | . . . . 5 | |
6 | 5 | nfcri 2273 | . . . 4 |
7 | iunxpf.4 | . . . . 5 | |
8 | 7 | eleq2d 2207 | . . . 4 |
9 | 2, 4, 6, 8 | rexxpf 4681 | . . 3 |
10 | eliun 3812 | . . 3 | |
11 | eliun 3812 | . . . 4 | |
12 | eliun 3812 | . . . . 5 | |
13 | 12 | rexbii 2440 | . . . 4 |
14 | 11, 13 | bitri 183 | . . 3 |
15 | 9, 10, 14 | 3bitr4i 211 | . 2 |
16 | 15 | eqriv 2134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wnfc 2266 wrex 2415 cop 3525 ciun 3808 cxp 4532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-iun 3810 df-opab 3985 df-xp 4540 df-rel 4541 |
This theorem is referenced by: dfmpo 6113 |
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