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Mirrors > Home > ILE Home > Th. List > ot1stg | Unicode version |
Description: Extract the first member of an ordered triple. (Due to infrequent usage, it isn't worthwhile at this point to define special extractors for triples, so we reuse the ordered pair extractors for ot1stg 5779, ot2ndg 5780, ot3rdgg 5781.) (Contributed by NM, 3-Apr-2015.) (Revised by Mario Carneiro, 2-May-2015.) |
Ref | Expression |
---|---|
ot1stg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ot 3385 | . . . . 5 | |
2 | 1 | fveq2i 5181 | . . . 4 |
3 | opexg 3964 | . . . . . 6 | |
4 | op1stg 5777 | . . . . . 6 | |
5 | 3, 4 | sylan 267 | . . . . 5 |
6 | 5 | 3impa 1099 | . . . 4 |
7 | 2, 6 | syl5eq 2084 | . . 3 |
8 | 7 | fveq2d 5182 | . 2 |
9 | op1stg 5777 | . . 3 | |
10 | 9 | 3adant3 924 | . 2 |
11 | 8, 10 | eqtrd 2072 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wcel 1393 cvv 2557 cop 3378 cotp 3379 cfv 4902 c1st 5765 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-ot 3385 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-iota 4867 df-fun 4904 df-fv 4910 df-1st 5767 |
This theorem is referenced by: (None) |
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