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Mirrors > Home > ILE Home > Th. List > ovmpt4g | Unicode version |
Description: Value of a function given by the maps-to notation. (This is the operation analog of fvmpt2 5642.) (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
ovmpt4g.3 |
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Ref | Expression |
---|---|
ovmpt4g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2774 |
. . 3
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2 | moeq 2936 |
. . . . . . 7
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3 | 2 | a1i 9 |
. . . . . 6
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4 | ovmpt4g.3 |
. . . . . . 7
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5 | df-mpo 5924 |
. . . . . . 7
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6 | 4, 5 | eqtri 2214 |
. . . . . 6
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7 | 3, 6 | ovidi 6038 |
. . . . 5
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8 | eqeq2 2203 |
. . . . 5
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9 | 7, 8 | mpbidi 151 |
. . . 4
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10 | 9 | exlimdv 1830 |
. . 3
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11 | 1, 10 | syl5 32 |
. 2
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12 | 11 | 3impia 1202 |
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-in1 615 ax-in2 616 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 2167 ax-ext 2175 ax-sep 4148 ax-pow 4204 ax-pr 4239 ax-setind 4570 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2045 df-mo 2046 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ne 2365 df-ral 2477 df-rex 2478 df-v 2762 df-sbc 2987 df-dif 3156 df-un 3158 df-in 3160 df-ss 3167 df-pw 3604 df-sn 3625 df-pr 3626 df-op 3628 df-uni 3837 df-br 4031 df-opab 4092 df-id 4325 df-xp 4666 df-rel 4667 df-cnv 4668 df-co 4669 df-dm 4670 df-iota 5216 df-fun 5257 df-fv 5263 df-ov 5922 df-oprab 5923 df-mpo 5924 |
This theorem is referenced by: ovmpos 6043 ov2gf 6044 ovmpodxf 6045 ovmpodf 6051 ofmres 6190 fnmpoovd 6270 mapxpen 6906 cnmpt21 14470 cnmpt2t 14472 cnmptcom 14477 |
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