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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 5254.) (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
ovmpt4g.3 |
Ref | Expression |
---|---|
ovmpt4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . . 3 | |
2 | moeq 2716 | . . . . . . 7 | |
3 | 2 | a1i 9 | . . . . . 6 |
4 | ovmpt4g.3 | . . . . . . 7 | |
5 | df-mpt2 5517 | . . . . . . 7 | |
6 | 4, 5 | eqtri 2060 | . . . . . 6 |
7 | 3, 6 | ovidi 5619 | . . . . 5 |
8 | eqeq2 2049 | . . . . 5 | |
9 | 7, 8 | mpbidi 140 | . . . 4 |
10 | 9 | exlimdv 1700 | . . 3 |
11 | 1, 10 | syl5 28 | . 2 |
12 | 11 | 3impia 1101 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wex 1381 wcel 1393 wmo 1901 (class class class)co 5512 coprab 5513 cmpt2 5514 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-setind 4262 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 |
This theorem is referenced by: ovmpt2s 5624 ov2gf 5625 ovmpt2dxf 5626 ovmpt2df 5632 ofmres 5763 |
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