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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 4664 |
. . . . 5
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2 | 1 | anbi1i 458 |
. . . 4
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3 | 19.41vv 1915 |
. . . 4
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4 | anass 401 |
. . . . . 6
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5 | rabxp.1 |
. . . . . . . . 9
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6 | 5 | anbi2d 464 |
. . . . . . . 8
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7 | df-3an 982 |
. . . . . . . 8
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8 | 6, 7 | bitr4di 198 |
. . . . . . 7
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9 | 8 | pm5.32i 454 |
. . . . . 6
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10 | 4, 9 | bitri 184 |
. . . . 5
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11 | 10 | 2exbii 1617 |
. . . 4
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12 | 2, 3, 11 | 3bitr2i 208 |
. . 3
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13 | 12 | abbii 2305 |
. 2
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14 | df-rab 2477 |
. 2
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15 | df-opab 4083 |
. 2
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16 | 13, 14, 15 | 3eqtr4i 2220 |
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 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-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-opab 4083 df-xp 4653 |
This theorem is referenced by: (None) |
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