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Mirrors > Home > ILE Home > Th. List > riinint | Unicode version |
Description: Express a relative indexed intersection as an intersection. (Contributed by Stefan O'Rear, 22-Feb-2015.) |
Ref | Expression |
---|---|
riinint |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssexg 4067 | . . . . . . 7 | |
2 | 1 | expcom 115 | . . . . . 6 |
3 | 2 | ralimdv 2500 | . . . . 5 |
4 | 3 | imp 123 | . . . 4 |
5 | dfiin3g 4797 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | 6 | ineq2d 3277 | . 2 |
8 | intun 3802 | . . 3 | |
9 | intsng 3805 | . . . . 5 | |
10 | 9 | adantr 274 | . . . 4 |
11 | 10 | ineq1d 3276 | . . 3 |
12 | 8, 11 | syl5eq 2184 | . 2 |
13 | 7, 12 | eqtr4d 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 wral 2416 cvv 2686 cun 3069 cin 3070 wss 3071 csn 3527 cint 3771 ciin 3814 cmpt 3989 crn 4540 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-int 3772 df-iin 3816 df-br 3930 df-opab 3990 df-mpt 3991 df-cnv 4547 df-dm 4549 df-rn 4550 |
This theorem is referenced by: (None) |
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