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Mirrors > Home > ILE Home > Th. List > elovmpo | Unicode version |
Description: Utility lemma for two-parameter classes. (Contributed by Stefan O'Rear, 21-Jan-2015.) |
Ref | Expression |
---|---|
elovmpo.d | |
elovmpo.c | |
elovmpo.e |
Ref | Expression |
---|---|
elovmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elovmpo.d | . . . 4 | |
2 | 1 | elmpocl 6044 | . . 3 |
3 | elovmpo.c | . . . . . . 7 | |
4 | 3 | gen2 1443 | . . . . . 6 |
5 | elovmpo.e | . . . . . . . 8 | |
6 | 5 | eleq1d 2239 | . . . . . . 7 |
7 | 6 | spc2gv 2821 | . . . . . 6 |
8 | 4, 7 | mpi 15 | . . . . 5 |
9 | 5, 1 | ovmpoga 5979 | . . . . 5 |
10 | 8, 9 | mpd3an3 1333 | . . . 4 |
11 | 10 | eleq2d 2240 | . . 3 |
12 | 2, 11 | biadan2 453 | . 2 |
13 | df-3an 975 | . 2 | |
14 | 12, 13 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wal 1346 wceq 1348 wcel 2141 cvv 2730 (class class class)co 5850 cmpo 5852 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-setind 4519 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 df-ov 5853 df-oprab 5854 df-mpo 5855 |
This theorem is referenced by: (None) |
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