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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 2671 | . 2 | |
2 | elex 2671 | . 2 | |
3 | df-3an 949 | . . . . . 6 | |
4 | 3 | baibr 890 | . . . . 5 |
5 | 4 | abbidv 2235 | . . . 4 |
6 | abid2 2238 | . . . 4 | |
7 | df-op 3506 | . . . . 5 | |
8 | 7 | eqcomi 2121 | . . . 4 |
9 | 5, 6, 8 | 3eqtr3g 2173 | . . 3 |
10 | 9 | eqcomd 2123 | . 2 |
11 | 1, 2, 10 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wceq 1316 wcel 1465 cab 2103 cvv 2660 csn 3497 cpr 3498 cop 3500 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 df-op 3506 |
This theorem is referenced by: dfop 3674 opexg 4120 opth1 4128 opth 4129 0nelop 4140 op1stbg 4370 |
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