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Mirrors > Home > ILE Home > Th. List > ovmpos | Unicode version |
Description: Value of a function given by the maps-to notation, expressed using explicit substitution. (Contributed by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
ovmpos.3 |
Ref | Expression |
---|---|
ovmpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2723 | . . 3 | |
2 | nfcv 2299 | . . . . 5 | |
3 | nfcv 2299 | . . . . 5 | |
4 | nfcv 2299 | . . . . 5 | |
5 | nfcsb1v 3064 | . . . . . . 7 | |
6 | 5 | nfel1 2310 | . . . . . 6 |
7 | ovmpos.3 | . . . . . . . . 9 | |
8 | nfmpo1 5890 | . . . . . . . . 9 | |
9 | 7, 8 | nfcxfr 2296 | . . . . . . . 8 |
10 | nfcv 2299 | . . . . . . . 8 | |
11 | 2, 9, 10 | nfov 5853 | . . . . . . 7 |
12 | 11, 5 | nfeq 2307 | . . . . . 6 |
13 | 6, 12 | nfim 1552 | . . . . 5 |
14 | nfcsb1v 3064 | . . . . . . 7 | |
15 | 14 | nfel1 2310 | . . . . . 6 |
16 | nfmpo2 5891 | . . . . . . . . 9 | |
17 | 7, 16 | nfcxfr 2296 | . . . . . . . 8 |
18 | 3, 17, 4 | nfov 5853 | . . . . . . 7 |
19 | 18, 14 | nfeq 2307 | . . . . . 6 |
20 | 15, 19 | nfim 1552 | . . . . 5 |
21 | csbeq1a 3040 | . . . . . . 7 | |
22 | 21 | eleq1d 2226 | . . . . . 6 |
23 | oveq1 5833 | . . . . . . 7 | |
24 | 23, 21 | eqeq12d 2172 | . . . . . 6 |
25 | 22, 24 | imbi12d 233 | . . . . 5 |
26 | csbeq1a 3040 | . . . . . . 7 | |
27 | 26 | eleq1d 2226 | . . . . . 6 |
28 | oveq2 5834 | . . . . . . 7 | |
29 | 28, 26 | eqeq12d 2172 | . . . . . 6 |
30 | 27, 29 | imbi12d 233 | . . . . 5 |
31 | 7 | ovmpt4g 5945 | . . . . . 6 |
32 | 31 | 3expia 1187 | . . . . 5 |
33 | 2, 3, 4, 13, 20, 25, 30, 32 | vtocl2gaf 2779 | . . . 4 |
34 | csbcomg 3054 | . . . . 5 | |
35 | 34 | eleq1d 2226 | . . . 4 |
36 | 34 | eqeq2d 2169 | . . . 4 |
37 | 33, 35, 36 | 3imtr4d 202 | . . 3 |
38 | 1, 37 | syl5 32 | . 2 |
39 | 38 | 3impia 1182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wceq 1335 wcel 2128 cvv 2712 csb 3031 (class class class)co 5826 cmpo 5828 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-setind 4498 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-iota 5137 df-fun 5174 df-fv 5180 df-ov 5829 df-oprab 5830 df-mpo 5831 |
This theorem is referenced by: (None) |
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