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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2741 | . 2 | |
2 | elex 2741 | . 2 | |
3 | df-3an 975 | . . . . . 6 | |
4 | 3 | baibr 915 | . . . . 5 |
5 | 4 | abbidv 2288 | . . . 4 |
6 | abid2 2291 | . . . 4 | |
7 | df-op 3592 | . . . . 5 | |
8 | 7 | eqcomi 2174 | . . . 4 |
9 | 5, 6, 8 | 3eqtr3g 2226 | . . 3 |
10 | 9 | eqcomd 2176 | . 2 |
11 | 1, 2, 10 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 973 wceq 1348 wcel 2141 cab 2156 cvv 2730 csn 3583 cpr 3584 cop 3586 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 df-op 3592 |
This theorem is referenced by: dfop 3764 opexg 4213 opth1 4221 opth 4222 0nelop 4233 op1stbg 4464 |
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