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Mirrors > Home > ILE Home > Th. List > rnmpt | Unicode version |
Description: The range of a function in maps-to notation. (Contributed by Scott Fenton, 21-Mar-2011.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
rnmpt.1 |
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Ref | Expression |
---|---|
rnmpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rnopab 4895 |
. 2
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2 | rnmpt.1 |
. . . 4
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3 | df-mpt 4084 |
. . . 4
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4 | 2, 3 | eqtri 2210 |
. . 3
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5 | 4 | rneqi 4876 |
. 2
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6 | df-rex 2474 |
. . 3
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7 | 6 | abbii 2305 |
. 2
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8 | 1, 5, 7 | 3eqtr4i 2220 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-br 4022 df-opab 4083 df-mpt 4084 df-cnv 4655 df-dm 4657 df-rn 4658 |
This theorem is referenced by: elrnmpt 4897 elrnmpt1 4899 elrnmptg 4900 dfiun3g 4905 dfiin3g 4906 fnrnfv 5586 fmpt 5690 fnasrn 5718 fnasrng 5720 fliftf 5824 abrexex 6146 abrexexg 6147 fo1st 6186 fo2nd 6187 qliftf 6650 negfi 11277 4sqlem11 12444 4sqlem12 12445 quslem 12812 restco 14159 |
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