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Mirrors > Home > ILE Home > Th. List > dfopg | Unicode version |
Description: Value of the ordered pair when the arguments are sets. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
dfopg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. 2
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2 | elex 2700 |
. 2
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3 | df-3an 965 |
. . . . . 6
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4 | 3 | baibr 906 |
. . . . 5
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5 | 4 | abbidv 2258 |
. . . 4
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6 | abid2 2261 |
. . . 4
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7 | df-op 3541 |
. . . . 5
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8 | 7 | eqcomi 2144 |
. . . 4
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9 | 5, 6, 8 | 3eqtr3g 2196 |
. . 3
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10 | 9 | eqcomd 2146 |
. 2
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11 | 1, 2, 10 | syl2an 287 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 df-op 3541 |
This theorem is referenced by: dfop 3712 opexg 4158 opth1 4166 opth 4167 0nelop 4178 op1stbg 4408 |
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