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Mirrors > Home > ILE Home > Th. List > opabbrex | Unicode version |
Description: A collection of ordered pairs with an extension of a binary relation is a set. (Contributed by Alexander van der Vekens, 1-Nov-2017.) |
Ref | Expression |
---|---|
opabbrex.1 |
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opabbrex.2 |
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Ref | Expression |
---|---|
opabbrex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-opab 4062 |
. . 3
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2 | opabbrex.2 |
. . 3
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3 | 1, 2 | eqeltrrid 2265 |
. 2
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4 | df-opab 4062 |
. . 3
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5 | opabbrex.1 |
. . . . . . 7
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6 | 5 | adantrd 279 |
. . . . . 6
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7 | 6 | anim2d 337 |
. . . . 5
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8 | 7 | 2eximdv 1882 |
. . . 4
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9 | 8 | ss2abdv 3228 |
. . 3
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10 | 4, 9 | eqsstrid 3201 |
. 2
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11 | 3, 10 | ssexd 4140 |
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-ext 2159 ax-sep 4118 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-opab 4062 |
This theorem is referenced by: (None) |
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