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Mirrors > Home > ILE Home > Th. List > ovprc | Unicode version |
Description: The value of an operation when the one of the arguments is a proper class. Note: this theorem is dependent on our particular definitions of operation value, function value, and ordered pair. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
ovprc1.1 |
Ref | Expression |
---|---|
ovprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5745 | . 2 | |
2 | opprc 3696 | . . . 4 | |
3 | 0ex 4025 | . . . 4 | |
4 | 2, 3 | syl6eqel 2208 | . . 3 |
5 | df-br 3900 | . . . . 5 | |
6 | ovprc1.1 | . . . . . 6 | |
7 | brrelex12 4547 | . . . . . 6 | |
8 | 6, 7 | mpan 420 | . . . . 5 |
9 | 5, 8 | sylbir 134 | . . . 4 |
10 | 9 | con3i 606 | . . 3 |
11 | ndmfvg 5420 | . . 3 | |
12 | 4, 10, 11 | syl2anc 408 | . 2 |
13 | 1, 12 | syl5eq 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1316 wcel 1465 cvv 2660 c0 3333 cop 3500 class class class wbr 3899 cdm 4509 wrel 4514 cfv 5093 (class class class)co 5742 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-dm 4519 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: ovprc1 5775 ovprc2 5776 |
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