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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 2748 |
. 2
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2 | elex 2748 |
. 2
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3 | df-3an 980 |
. . . . . 6
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4 | 3 | baibr 920 |
. . . . 5
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5 | 4 | abbidv 2295 |
. . . 4
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6 | abid2 2298 |
. . . 4
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7 | df-op 3601 |
. . . . 5
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8 | 7 | eqcomi 2181 |
. . . 4
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9 | 5, 6, 8 | 3eqtr3g 2233 |
. . 3
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10 | 9 | eqcomd 2183 |
. 2
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11 | 1, 2, 10 | syl2an 289 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2739 df-op 3601 |
This theorem is referenced by: dfop 3777 opexg 4228 opth1 4236 opth 4237 0nelop 4248 op1stbg 4479 |
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