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Mirrors > Home > MPE Home > Th. List > riotass | Structured version Visualization version 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 3908 | . . . 4 | |
2 | riotasbc 6626 | . . . 4 | |
3 | 1, 2 | syl 17 | . . 3 |
4 | simp1 1061 | . . . . 5 | |
5 | riotacl 6625 | . . . . . 6 | |
6 | 1, 5 | syl 17 | . . . . 5 |
7 | 4, 6 | sseldd 3604 | . . . 4 |
8 | simp3 1063 | . . . 4 | |
9 | nfriota1 6618 | . . . . 5 | |
10 | 9 | nfsbc1 3454 | . . . . 5 |
11 | sbceq1a 3446 | . . . . 5 | |
12 | 9, 10, 11 | riota2f 6632 | . . . 4 |
13 | 7, 8, 12 | syl2anc 693 | . . 3 |
14 | 3, 13 | mpbid 222 | . 2 |
15 | 14 | eqcomd 2628 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 w3a 1037 wceq 1483 wcel 1990 wrex 2913 wreu 2914 wsbc 3435 wss 3574 crio 6610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-un 3579 df-in 3581 df-ss 3588 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: moriotass 6640 |
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