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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 5737. (Contributed by NM, 23-Sep-2007.) |
Ref | Expression |
---|---|
fvsnun.1 |
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fvsnun.2 |
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fvsnun.3 |
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Ref | Expression |
---|---|
fvsnun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvsnun.3 |
. . . . 5
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2 | 1 | reseq1i 4924 |
. . . 4
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3 | resundir 4942 |
. . . 4
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4 | disjdif 3510 |
. . . . . . 7
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5 | fvsnun.1 |
. . . . . . . . 9
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6 | fvsnun.2 |
. . . . . . . . 9
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7 | 5, 6 | fnsn 5292 |
. . . . . . . 8
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8 | fnresdisj 5348 |
. . . . . . . 8
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9 | 7, 8 | ax-mp 5 |
. . . . . . 7
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10 | 4, 9 | mpbi 145 |
. . . . . 6
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11 | residm 4960 |
. . . . . 6
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12 | 10, 11 | uneq12i 3302 |
. . . . 5
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13 | uncom 3294 |
. . . . 5
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14 | un0 3471 |
. . . . 5
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15 | 12, 13, 14 | 3eqtri 2214 |
. . . 4
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16 | 2, 3, 15 | 3eqtri 2214 |
. . 3
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17 | 16 | fveq1i 5538 |
. 2
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18 | fvres 5561 |
. 2
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19 | fvres 5561 |
. 2
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20 | 17, 18, 19 | 3eqtr3a 2246 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-br 4022 df-opab 4083 df-id 4314 df-xp 4653 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-res 4659 df-iota 5199 df-fun 5240 df-fn 5241 df-fv 5246 |
This theorem is referenced by: facnn 10748 |
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