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Mirrors > Home > ILE Home > Th. List > rabxp | Unicode version |
Description: Membership in a class builder restricted to a cross product. (Contributed by NM, 20-Feb-2014.) |
Ref | Expression |
---|---|
rabxp.1 |
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Ref | Expression |
---|---|
rabxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxp 4305 |
. . . . 5
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2 | 1 | anbi1i 431 |
. . . 4
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3 | 19.41vv 1780 |
. . . 4
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4 | anass 381 |
. . . . . 6
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5 | rabxp.1 |
. . . . . . . . 9
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6 | 5 | anbi2d 437 |
. . . . . . . 8
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7 | df-3an 886 |
. . . . . . . 8
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8 | 6, 7 | syl6bbr 187 |
. . . . . . 7
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9 | 8 | pm5.32i 427 |
. . . . . 6
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10 | 4, 9 | bitri 173 |
. . . . 5
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11 | 10 | 2exbii 1494 |
. . . 4
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12 | 2, 3, 11 | 3bitr2i 197 |
. . 3
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13 | 12 | abbii 2150 |
. 2
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14 | df-rab 2309 |
. 2
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15 | df-opab 3810 |
. 2
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16 | 13, 14, 15 | 3eqtr4i 2067 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rab 2309 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-opab 3810 df-xp 4294 |
This theorem is referenced by: (None) |
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