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Mirrors > Home > ILE Home > Th. List > iota1 | Unicode version |
Description: Property of iota. (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
iota1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2016 | . 2 | |
2 | sp 1498 | . . . . 5 | |
3 | iotaval 5158 | . . . . . 6 | |
4 | 3 | eqeq2d 2176 | . . . . 5 |
5 | 2, 4 | bitr4d 190 | . . . 4 |
6 | eqcom 2166 | . . . 4 | |
7 | 5, 6 | bitrdi 195 | . . 3 |
8 | 7 | exlimiv 1585 | . 2 |
9 | 1, 8 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 wex 1479 weu 2013 cio 5145 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-sn 3576 df-pr 3577 df-uni 3784 df-iota 5147 |
This theorem is referenced by: iota2df 5171 sniota 5174 tz6.12-1 5507 riota1 5810 riota1a 5811 erovlem 6584 |
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