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Mirrors > Home > ILE Home > Th. List > iunxprg | Unicode version |
Description: A pair index picks out two instances of an indexed union's argument. (Contributed by Alexander van der Vekens, 2-Feb-2018.) |
Ref | Expression |
---|---|
iunxprg.1 | |
iunxprg.2 |
Ref | Expression |
---|---|
iunxprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3534 | . . . 4 | |
2 | iuneq1 3826 | . . . 4 | |
3 | 1, 2 | ax-mp 5 | . . 3 |
4 | iunxun 3892 | . . 3 | |
5 | 3, 4 | eqtri 2160 | . 2 |
6 | iunxprg.1 | . . . . 5 | |
7 | 6 | iunxsng 3888 | . . . 4 |
8 | 7 | adantr 274 | . . 3 |
9 | iunxprg.2 | . . . . 5 | |
10 | 9 | iunxsng 3888 | . . . 4 |
11 | 10 | adantl 275 | . . 3 |
12 | 8, 11 | uneq12d 3231 | . 2 |
13 | 5, 12 | syl5eq 2184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cun 3069 csn 3527 cpr 3528 ciun 3813 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-iun 3815 |
This theorem is referenced by: unct 11959 |
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