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Mirrors > Home > ILE Home > Th. List > mpteq2da | Unicode version |
Description: Slightly more general equality inference for the maps-to notation. (Contributed by FL, 14-Sep-2013.) (Revised by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq2da.1 | |
mpteq2da.2 |
Ref | Expression |
---|---|
mpteq2da |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2140 | . . 3 | |
2 | 1 | ax-gen 1426 | . 2 |
3 | mpteq2da.1 | . . 3 | |
4 | mpteq2da.2 | . . . 4 | |
5 | 4 | ex 114 | . . 3 |
6 | 3, 5 | ralrimi 2506 | . 2 |
7 | mpteq12f 4016 | . 2 | |
8 | 2, 6, 7 | sylancr 411 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1330 wceq 1332 wnf 1437 wcel 1481 wral 2417 cmpt 3997 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-opab 3998 df-mpt 3999 |
This theorem is referenced by: mpteq2dva 4026 prodeq1f 11353 prodeq2 11358 |
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