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Mirrors > Home > ILE Home > Th. List > riotass | Unicode version |
Description: Restriction of a unique element to a smaller class. (Contributed by NM, 19-Oct-2005.) (Revised by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
riotass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reuss 3352 | . . . 4 | |
2 | riotasbc 5738 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | simp1 981 | . . . . 5 | |
5 | riotacl 5737 | . . . . . 6 | |
6 | 1, 5 | syl 14 | . . . . 5 |
7 | 4, 6 | sseldd 3093 | . . . 4 |
8 | simp3 983 | . . . 4 | |
9 | nfriota1 5730 | . . . . 5 | |
10 | 9 | nfsbc1 2921 | . . . . 5 |
11 | sbceq1a 2913 | . . . . 5 | |
12 | 9, 10, 11 | riota2f 5744 | . . . 4 |
13 | 7, 8, 12 | syl2anc 408 | . . 3 |
14 | 3, 13 | mpbid 146 | . 2 |
15 | 14 | eqcomd 2143 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wceq 1331 wcel 1480 wrex 2415 wreu 2416 wsbc 2904 wss 3066 crio 5722 |
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-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-uni 3732 df-iota 5083 df-riota 5723 |
This theorem is referenced by: moriotass 5751 |
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