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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 3588 | . . . 4 | |
2 | iuneq1 3884 | . . . 4 | |
3 | 1, 2 | ax-mp 5 | . . 3 |
4 | iunxun 3950 | . . 3 | |
5 | 3, 4 | eqtri 2191 | . 2 |
6 | iunxprg.1 | . . . . 5 | |
7 | 6 | iunxsng 3946 | . . . 4 |
8 | 7 | adantr 274 | . . 3 |
9 | iunxprg.2 | . . . . 5 | |
10 | 9 | iunxsng 3946 | . . . 4 |
11 | 10 | adantl 275 | . . 3 |
12 | 8, 11 | uneq12d 3282 | . 2 |
13 | 5, 12 | eqtrid 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 cun 3119 csn 3581 cpr 3582 ciun 3871 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-pr 3588 df-iun 3873 |
This theorem is referenced by: unct 12384 |
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