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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 |
Ref | Expression |
---|---|
mpteq2ia |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2117 | . . 3 | |
2 | 1 | ax-gen 1410 | . 2 |
3 | mpteq2ia.1 | . . 3 | |
4 | 3 | rgen 2462 | . 2 |
5 | mpteq12f 3978 | . 2 | |
6 | 2, 4, 5 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1314 wceq 1316 wcel 1465 wral 2393 cmpt 3959 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-ral 2398 df-opab 3960 df-mpt 3961 |
This theorem is referenced by: mpteq2i 3985 feqresmpt 5443 elfvmptrab 5484 fmptap 5578 offres 6001 cnrecnv 10650 ege2le3 11304 eirraplem 11410 cnmpt1st 12384 cnmpt2nd 12385 expcncf 12688 dvexp 12771 dveflem 12782 dvef 12783 |
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