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Mirrors > Home > ILE Home > Th. List > ot2ndg | Unicode version |
Description: Extract the second member of an ordered triple. (See ot1stg 6018 comment.) (Contributed by NM, 3-Apr-2015.) (Revised by Mario Carneiro, 2-May-2015.) |
Ref | Expression |
---|---|
ot2ndg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ot 3507 | . . . . 5 | |
2 | 1 | fveq2i 5392 | . . . 4 |
3 | opexg 4120 | . . . . . 6 | |
4 | op1stg 6016 | . . . . . 6 | |
5 | 3, 4 | sylan 281 | . . . . 5 |
6 | 5 | 3impa 1161 | . . . 4 |
7 | 2, 6 | syl5eq 2162 | . . 3 |
8 | 7 | fveq2d 5393 | . 2 |
9 | op2ndg 6017 | . . 3 | |
10 | 9 | 3adant3 986 | . 2 |
11 | 8, 10 | eqtrd 2150 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wceq 1316 wcel 1465 cvv 2660 cop 3500 cotp 3501 cfv 5093 c1st 6004 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-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-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 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-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-ot 3507 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-1st 6006 df-2nd 6007 |
This theorem is referenced by: (None) |
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