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Mirrors > Home > ILE Home > Th. List > ressid | Unicode version |
Description: Behavior of trivial restriction. (Contributed by Stefan O'Rear, 29-Nov-2014.) |
Ref | Expression |
---|---|
ressid.1 |
Ref | Expression |
---|---|
ressid | ↾s |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3112 | . 2 | |
2 | id 19 | . 2 | |
3 | ressid.1 | . . 3 | |
4 | baseid 12001 | . . . . 5 Slot | |
5 | basendxnn 12003 | . . . . . 6 | |
6 | 5 | a1i 9 | . . . . 5 |
7 | 4, 2, 6 | strnfvnd 11968 | . . . 4 |
8 | fvexg 5433 | . . . . 5 | |
9 | 5, 8 | mpan2 421 | . . . 4 |
10 | 7, 9 | eqeltrd 2214 | . . 3 |
11 | 3, 10 | eqeltrid 2224 | . 2 |
12 | eqid 2137 | . . 3 ↾s ↾s | |
13 | 12, 3 | ressid2 12007 | . 2 ↾s |
14 | 1, 2, 11, 13 | mp3an2i 1320 | 1 ↾s |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cvv 2681 wss 3066 cfv 5118 (class class class)co 5767 cn 8713 cnx 11945 cbs 11948 ↾s cress 11949 |
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-in1 603 ax-in2 604 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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 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-ne 2307 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-if 3470 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-int 3767 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-iota 5083 df-fun 5120 df-fv 5126 df-ov 5770 df-oprab 5771 df-mpo 5772 df-inn 8714 df-ndx 11951 df-slot 11952 df-base 11954 df-ress 11956 |
This theorem is referenced by: (None) |
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