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Mirrors > Home > ILE Home > Th. List > mpteq2ia | Unicode version |
Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq2ia.1 |
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Ref | Expression |
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mpteq2ia |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2100 |
. . 3
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2 | 1 | ax-gen 1393 |
. 2
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3 | mpteq2ia.1 |
. . 3
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4 | 3 | rgen 2444 |
. 2
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5 | mpteq12f 3948 |
. 2
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6 | 2, 4, 5 | mp2an 420 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-11 1452 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-ral 2380 df-opab 3930 df-mpt 3931 |
This theorem is referenced by: mpteq2i 3955 feqresmpt 5407 elfvmptrab 5448 fmptap 5542 offres 5964 cnrecnv 10523 ege2le3 11175 eirraplem 11278 cnmpt1st 12238 cnmpt2nd 12239 expcncf 12504 |
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