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Mirrors > Home > ILE Home > Th. List > dfmpt3 | Unicode version |
Description: Alternate definition for the maps-to notation df-mpt 4052. (Contributed by Mario Carneiro, 30-Dec-2016.) |
Ref | Expression |
---|---|
dfmpt3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4052 | . 2 | |
2 | velsn 3600 | . . . . . . 7 | |
3 | 2 | anbi2i 454 | . . . . . 6 |
4 | 3 | anbi2i 454 | . . . . 5 |
5 | 4 | 2exbii 1599 | . . . 4 |
6 | eliunxp 4750 | . . . 4 | |
7 | elopab 4243 | . . . 4 | |
8 | 5, 6, 7 | 3bitr4i 211 | . . 3 |
9 | 8 | eqriv 2167 | . 2 |
10 | 1, 9 | eqtr4i 2194 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 csn 3583 cop 3586 ciun 3873 copab 4049 cmpt 4050 cxp 4609 |
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 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 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-iun 3875 df-opab 4051 df-mpt 4052 df-xp 4617 df-rel 4618 |
This theorem is referenced by: dfmpt 5673 dfmptg 5675 |
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