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Mirrors > Home > ILE Home > Th. List > dfmpt3 | Unicode version |
Description: Alternate definition for the maps-to notation df-mpt 4029. (Contributed by Mario Carneiro, 30-Dec-2016.) |
Ref | Expression |
---|---|
dfmpt3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4029 | . 2 | |
2 | velsn 3578 | . . . . . . 7 | |
3 | 2 | anbi2i 453 | . . . . . 6 |
4 | 3 | anbi2i 453 | . . . . 5 |
5 | 4 | 2exbii 1586 | . . . 4 |
6 | eliunxp 4727 | . . . 4 | |
7 | elopab 4220 | . . . 4 | |
8 | 5, 6, 7 | 3bitr4i 211 | . . 3 |
9 | 8 | eqriv 2154 | . 2 |
10 | 1, 9 | eqtr4i 2181 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wex 1472 wcel 2128 csn 3561 cop 3564 ciun 3851 copab 4026 cmpt 4027 cxp 4586 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-iun 3853 df-opab 4028 df-mpt 4029 df-xp 4594 df-rel 4595 |
This theorem is referenced by: dfmpt 5646 dfmptg 5648 |
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