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Mirrors > Home > ILE Home > Th. List > fvsnun1 | Unicode version |
Description: The value of a function with one of its ordered pairs replaced, at the replaced ordered pair. See also fvsnun2 5680. (Contributed by NM, 23-Sep-2007.) |
Ref | Expression |
---|---|
fvsnun.1 | |
fvsnun.2 | |
fvsnun.3 |
Ref | Expression |
---|---|
fvsnun1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvsnun.3 | . . . . 5 | |
2 | 1 | reseq1i 4877 | . . . 4 |
3 | resundir 4895 | . . . . 5 | |
4 | incom 3312 | . . . . . . . . 9 | |
5 | disjdif 3479 | . . . . . . . . 9 | |
6 | 4, 5 | eqtri 2185 | . . . . . . . 8 |
7 | resdisj 5029 | . . . . . . . 8 | |
8 | 6, 7 | ax-mp 5 | . . . . . . 7 |
9 | 8 | uneq2i 3271 | . . . . . 6 |
10 | un0 3440 | . . . . . 6 | |
11 | 9, 10 | eqtri 2185 | . . . . 5 |
12 | 3, 11 | eqtri 2185 | . . . 4 |
13 | 2, 12 | eqtri 2185 | . . 3 |
14 | 13 | fveq1i 5484 | . 2 |
15 | fvsnun.1 | . . . 4 | |
16 | 15 | snid 3604 | . . 3 |
17 | fvres 5507 | . . 3 | |
18 | 16, 17 | ax-mp 5 | . 2 |
19 | fvres 5507 | . . . 4 | |
20 | 16, 19 | ax-mp 5 | . . 3 |
21 | fvsnun.2 | . . . 4 | |
22 | 15, 21 | fvsn 5677 | . . 3 |
23 | 20, 22 | eqtri 2185 | . 2 |
24 | 14, 18, 23 | 3eqtr3i 2193 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cvv 2724 cdif 3111 cun 3112 cin 3113 c0 3407 csn 3573 cop 3576 cres 4603 cfv 5185 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4097 ax-pow 4150 ax-pr 4184 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2726 df-sbc 2950 df-dif 3116 df-un 3118 df-in 3120 df-ss 3127 df-nul 3408 df-pw 3558 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-br 3980 df-opab 4041 df-id 4268 df-xp 4607 df-rel 4608 df-cnv 4609 df-co 4610 df-dm 4611 df-res 4613 df-iota 5150 df-fun 5187 df-fv 5193 |
This theorem is referenced by: fac0 10635 |
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