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Mirrors > Home > ILE Home > Th. List > fvsnun2 | Unicode version |
Description: The value of a function with one of its ordered pairs replaced, at arguments other than the replaced one. See also fvsnun1 5691. (Contributed by NM, 23-Sep-2007.) |
Ref | Expression |
---|---|
fvsnun.1 | |
fvsnun.2 | |
fvsnun.3 |
Ref | Expression |
---|---|
fvsnun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvsnun.3 | . . . . 5 | |
2 | 1 | reseq1i 4885 | . . . 4 |
3 | resundir 4903 | . . . 4 | |
4 | disjdif 3486 | . . . . . . 7 | |
5 | fvsnun.1 | . . . . . . . . 9 | |
6 | fvsnun.2 | . . . . . . . . 9 | |
7 | 5, 6 | fnsn 5250 | . . . . . . . 8 |
8 | fnresdisj 5306 | . . . . . . . 8 | |
9 | 7, 8 | ax-mp 5 | . . . . . . 7 |
10 | 4, 9 | mpbi 144 | . . . . . 6 |
11 | residm 4921 | . . . . . 6 | |
12 | 10, 11 | uneq12i 3279 | . . . . 5 |
13 | uncom 3271 | . . . . 5 | |
14 | un0 3447 | . . . . 5 | |
15 | 12, 13, 14 | 3eqtri 2195 | . . . 4 |
16 | 2, 3, 15 | 3eqtri 2195 | . . 3 |
17 | 16 | fveq1i 5495 | . 2 |
18 | fvres 5518 | . 2 | |
19 | fvres 5518 | . 2 | |
20 | 17, 18, 19 | 3eqtr3a 2227 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wcel 2141 cvv 2730 cdif 3118 cun 3119 cin 3120 c0 3414 csn 3581 cop 3584 cres 4611 wfn 5191 cfv 5196 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-res 4621 df-iota 5158 df-fun 5198 df-fn 5199 df-fv 5204 |
This theorem is referenced by: facnn 10654 |
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