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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 5612.) (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 2763 |
. . 3
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2 | moeq 2924 |
. . . . . . 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 5893 |
. . . . . . 7
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6 | 4, 5 | eqtri 2208 |
. . . . . 6
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7 | 3, 6 | ovidi 6006 |
. . . . 5
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8 | eqeq2 2197 |
. . . . 5
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9 | 7, 8 | mpbidi 151 |
. . . 4
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10 | 9 | exlimdv 1829 |
. . 3
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11 | 1, 10 | syl5 32 |
. 2
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12 | 11 | 3impia 1201 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-setind 4548 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-ral 2470 df-rex 2471 df-v 2751 df-sbc 2975 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-iota 5190 df-fun 5230 df-fv 5236 df-ov 5891 df-oprab 5892 df-mpo 5893 |
This theorem is referenced by: ovmpos 6011 ov2gf 6012 ovmpodxf 6013 ovmpodf 6019 ofmres 6150 fnmpoovd 6229 mapxpen 6861 cnmpt21 14062 cnmpt2t 14064 cnmptcom 14069 |
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