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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 2189 |
. . 3
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2 | 1 | ax-gen 1460 |
. 2
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3 | mpteq2ia.1 |
. . 3
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4 | 3 | rgen 2543 |
. 2
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5 | mpteq12f 4098 |
. 2
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6 | 2, 4, 5 | mp2an 426 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-opab 4080 df-mpt 4081 |
This theorem is referenced by: mpteq2i 4105 feqresmpt 5586 elfvmptrab 5627 fmptap 5722 offres 6154 cnrecnv 10937 ege2le3 11697 eirraplem 11802 cnmpt1st 14185 cnmpt2nd 14186 expcncf 14489 dvexp 14572 dveflem 14584 dvef 14585 |
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