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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 2723 | . 2 | |
2 | elex 2723 | . 2 | |
3 | df-3an 965 | . . . . . 6 | |
4 | 3 | baibr 906 | . . . . 5 |
5 | 4 | abbidv 2275 | . . . 4 |
6 | abid2 2278 | . . . 4 | |
7 | df-op 3569 | . . . . 5 | |
8 | 7 | eqcomi 2161 | . . . 4 |
9 | 5, 6, 8 | 3eqtr3g 2213 | . . 3 |
10 | 9 | eqcomd 2163 | . 2 |
11 | 1, 2, 10 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wceq 1335 wcel 2128 cab 2143 cvv 2712 csn 3560 cpr 3561 cop 3563 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 df-op 3569 |
This theorem is referenced by: dfop 3740 opexg 4188 opth1 4196 opth 4197 0nelop 4208 op1stbg 4439 |
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