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Mirrors > Home > ILE Home > Th. List > 2nd0 | Unicode version |
Description: The value of the second-member function at the empty set. (Contributed by NM, 23-Apr-2007.) |
Ref | Expression |
---|---|
2nd0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 4025 | . . 3 | |
2 | 2ndvalg 6009 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | dmsn0 4976 | . . . 4 | |
5 | dm0rn0 4726 | . . . 4 | |
6 | 4, 5 | mpbi 144 | . . 3 |
7 | 6 | unieqi 3716 | . 2 |
8 | uni0 3733 | . 2 | |
9 | 3, 7, 8 | 3eqtri 2142 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 cvv 2660 c0 3333 csn 3497 cuni 3706 cdm 4509 crn 4510 cfv 5093 c2nd 6005 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-iota 5058 df-fun 5095 df-fv 5101 df-2nd 6007 |
This theorem is referenced by: (None) |
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