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Mirrors > Home > ILE Home > Th. List > setsvalg | Unicode version |
Description: Value of the structure replacement function. (Contributed by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
setsvalg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2644 |
. 2
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2 | elex 2644 |
. 2
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3 | resexg 4785 |
. . . 4
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4 | snexg 4040 |
. . . 4
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5 | unexg 4293 |
. . . 4
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6 | 3, 4, 5 | syl2an 284 |
. . 3
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7 | simpl 108 |
. . . . . 6
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8 | simpr 109 |
. . . . . . . . 9
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9 | 8 | sneqd 3479 |
. . . . . . . 8
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10 | 9 | dmeqd 4669 |
. . . . . . 7
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11 | 10 | difeq2d 3133 |
. . . . . 6
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12 | 7, 11 | reseq12d 4746 |
. . . . 5
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13 | 12, 9 | uneq12d 3170 |
. . . 4
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14 | df-sets 11650 |
. . . 4
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15 | 13, 14 | ovmpt2ga 5812 |
. . 3
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16 | 6, 15 | mpd3an3 1281 |
. 2
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17 | 1, 2, 16 | syl2an 284 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-un 4284 ax-setind 4381 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-sbc 2855 df-dif 3015 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-opab 3922 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-res 4479 df-iota 5014 df-fun 5051 df-fv 5057 df-ov 5693 df-oprab 5694 df-mpt2 5695 df-sets 11650 |
This theorem is referenced by: setsvala 11674 setsfun 11678 setsfun0 11679 setsresg 11681 |
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