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Mirrors > Home > ILE Home > Th. List > mpteq1 | Unicode version |
Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2090 |
. . 3
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2 | 1 | rgen 2429 |
. 2
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3 | mpteq12 3927 |
. 2
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4 | 2, 3 | mpan2 417 |
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 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-ral 2365 df-opab 3906 df-mpt 3907 |
This theorem is referenced by: mpteq1d 3929 fmptap 5501 mpt2mpt 5754 mpt2mptsx 5981 mpt2mpts 5982 tposf12 6048 |
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