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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 5399.) (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 2634 |
. . 3
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2 | moeq 2791 |
. . . . . . 7
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3 | 2 | a1i 9 |
. . . . . 6
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4 | ovmpt4g.3 |
. . . . . . 7
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5 | df-mpt2 5671 |
. . . . . . 7
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6 | 4, 5 | eqtri 2109 |
. . . . . 6
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7 | 3, 6 | ovidi 5777 |
. . . . 5
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8 | eqeq2 2098 |
. . . . 5
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9 | 7, 8 | mpbidi 150 |
. . . 4
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10 | 9 | exlimdv 1748 |
. . 3
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11 | 1, 10 | syl5 32 |
. 2
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12 | 11 | 3impia 1141 |
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-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-setind 4366 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-ral 2365 df-rex 2366 df-v 2622 df-sbc 2842 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-id 4129 df-xp 4457 df-rel 4458 df-cnv 4459 df-co 4460 df-dm 4461 df-iota 4993 df-fun 5030 df-fv 5036 df-ov 5669 df-oprab 5670 df-mpt2 5671 |
This theorem is referenced by: ovmpt2s 5782 ov2gf 5783 ovmpt2dxf 5784 ovmpt2df 5790 ofmres 5921 mapxpen 6618 |
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