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Mirrors > Home > ILE Home > Th. List > iotass | Unicode version |
Description: Value of iota based on a proposition which holds only for values which are subsets of a given class. (Contributed by Mario Carneiro and Jim Kingdon, 21-Dec-2018.) |
Ref | Expression |
---|---|
iotass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iota 5083 | . 2 | |
2 | unieq 3740 | . . . . . . . 8 | |
3 | vex 2684 | . . . . . . . . 9 | |
4 | 3 | unisn 3747 | . . . . . . . 8 |
5 | 2, 4 | syl6eq 2186 | . . . . . . 7 |
6 | df-pw 3507 | . . . . . . . . . . 11 | |
7 | 6 | sseq2i 3119 | . . . . . . . . . 10 |
8 | ss2ab 3160 | . . . . . . . . . 10 | |
9 | 7, 8 | bitri 183 | . . . . . . . . 9 |
10 | 9 | biimpri 132 | . . . . . . . 8 |
11 | sspwuni 3892 | . . . . . . . 8 | |
12 | 10, 11 | sylib 121 | . . . . . . 7 |
13 | sseq1 3115 | . . . . . . . 8 | |
14 | 13 | biimpa 294 | . . . . . . 7 |
15 | 5, 12, 14 | syl2anr 288 | . . . . . 6 |
16 | 15 | ex 114 | . . . . 5 |
17 | 16 | ss2abdv 3165 | . . . 4 |
18 | df-pw 3507 | . . . 4 | |
19 | 17, 18 | sseqtrrdi 3141 | . . 3 |
20 | sspwuni 3892 | . . 3 | |
21 | 19, 20 | sylib 121 | . 2 |
22 | 1, 21 | eqsstrid 3138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 cab 2123 wss 3066 cpw 3505 csn 3522 cuni 3731 cio 5081 |
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 2119 |
This theorem depends on definitions: df-bi 116 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-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-uni 3732 df-iota 5083 |
This theorem is referenced by: fvss 5428 riotaexg 5727 |
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