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Mirrors > Home > ILE Home > Th. List > iotauni | Unicode version |
Description: Equivalence between two different forms of . (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iotauni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2009 | . 2 | |
2 | iotaval 5145 | . . . 4 | |
3 | uniabio 5144 | . . . 4 | |
4 | 2, 3 | eqtr4d 2193 | . . 3 |
5 | 4 | exlimiv 1578 | . 2 |
6 | 1, 5 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wceq 1335 wex 1472 weu 2006 cab 2143 cuni 3772 cio 5132 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-sn 3566 df-pr 3567 df-uni 3773 df-iota 5134 |
This theorem is referenced by: iotaint 5147 fveu 5459 riotauni 5783 |
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