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Mirrors > Home > ILE Home > Th. List > mpteq12dva | Unicode version |
Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 26-Jan-2017.) |
Ref | Expression |
---|---|
mpteq12dv.1 |
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mpteq12dva.2 |
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Ref | Expression |
---|---|
mpteq12dva |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpteq12dv.1 |
. . 3
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2 | 1 | alrimiv 1847 |
. 2
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3 | mpteq12dva.2 |
. . 3
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4 | 3 | ralrimiva 2508 |
. 2
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5 | mpteq12f 4016 |
. 2
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6 | 2, 4, 5 | syl2anc 409 |
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 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: mpteq12dv 4018 |
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