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Mirrors > Home > ILE Home > Th. List > dfoprab3 | Unicode version |
Description: Operation class abstraction expressed without existential quantifiers. (Contributed by NM, 16-Dec-2008.) |
Ref | Expression |
---|---|
dfoprab3.1 |
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Ref | Expression |
---|---|
dfoprab3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfoprab3s 6186 |
. 2
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2 | vex 2740 |
. . . . . 6
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3 | 1stexg 6163 |
. . . . . 6
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4 | 2, 3 | ax-mp 5 |
. . . . 5
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5 | 2ndexg 6164 |
. . . . . 6
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6 | 2, 5 | ax-mp 5 |
. . . . 5
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7 | eqcom 2179 |
. . . . . . . . . 10
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8 | eqcom 2179 |
. . . . . . . . . 10
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9 | 7, 8 | anbi12i 460 |
. . . . . . . . 9
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10 | eqopi 6168 |
. . . . . . . . 9
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11 | 9, 10 | sylan2b 287 |
. . . . . . . 8
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12 | dfoprab3.1 |
. . . . . . . 8
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13 | 11, 12 | syl 14 |
. . . . . . 7
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14 | 13 | bicomd 141 |
. . . . . 6
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15 | 14 | ex 115 |
. . . . 5
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16 | 4, 6, 15 | sbc2iedv 3035 |
. . . 4
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17 | 16 | pm5.32i 454 |
. . 3
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18 | 17 | opabbii 4068 |
. 2
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19 | 1, 18 | eqtr2i 2199 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4119 ax-pow 4172 ax-pr 4207 ax-un 4431 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3809 df-br 4002 df-opab 4063 df-mpt 4064 df-id 4291 df-xp 4630 df-rel 4631 df-cnv 4632 df-co 4633 df-dm 4634 df-rn 4635 df-iota 5175 df-fun 5215 df-fn 5216 df-f 5217 df-fo 5219 df-fv 5221 df-oprab 5874 df-1st 6136 df-2nd 6137 |
This theorem is referenced by: dfoprab4 6188 df1st2 6215 df2nd2 6216 |
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