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Mirrors > Home > ILE Home > Th. List > mpoeq123dv | Unicode version |
Description: An equality deduction for the maps-to notation. (Contributed by NM, 12-Sep-2011.) |
Ref | Expression |
---|---|
mpoeq123dv.1 |
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mpoeq123dv.2 |
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mpoeq123dv.3 |
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Ref | Expression |
---|---|
mpoeq123dv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpoeq123dv.1 |
. 2
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2 | mpoeq123dv.2 |
. . 3
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3 | 2 | adantr 276 |
. 2
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4 | mpoeq123dv.3 |
. . 3
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5 | 4 | adantr 276 |
. 2
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6 | 1, 3, 5 | mpoeq123dva 5935 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-oprab 5878 df-mpo 5879 |
This theorem is referenced by: mpoeq123i 5937 prdsex 12712 plusffvalg 12775 grpsubfvalg 12912 grpsubpropdg 12968 mulgfvalg 12979 mulgpropdg 13018 dvrfvald 13295 blfvalps 13816 |
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