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Mirrors > Home > ILE Home > Th. List > op1sta | Unicode version |
Description: Extract the first member of an ordered pair. (See op2nda 4825 to extract the second member and op1stb 4227 for an alternate version.) (Contributed by Raph Levien, 4-Dec-2003.) |
Ref | Expression |
---|---|
cnvsn.1 | |
cnvsn.2 |
Ref | Expression |
---|---|
op1sta |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.2 | . . . 4 | |
2 | 1 | dmsnop 4814 | . . 3 |
3 | 2 | unieqi 3611 | . 2 |
4 | cnvsn.1 | . . 3 | |
5 | 4 | unisn 3617 | . 2 |
6 | 3, 5 | eqtri 2101 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wcel 1433 cvv 2601 csn 3398 cop 3401 cuni 3601 cdm 4363 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-dm 4373 |
This theorem is referenced by: op1st 5793 fo1st 5804 f1stres 5806 xpassen 6327 xpdom2 6328 |
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